Radio communications system and method with increased transmission capacity

ABSTRACT

A radio communications method includes carrying out, by a transmitter: providing a digital time signal carrying digital symbols to be transmitted; and transmitting a radio frequency signal carrying the digital time signal. The method further includes carrying out, by a receiver: receiving the radio frequency signal transmitted by the transmitter; processing the received radio frequency signal to obtain a corresponding incoming digital signal; and extracting, from the incoming digital signal, the digital symbols carried by the incoming digital signal. The digital time signal carrying the digital symbols to be transmitted results from an approximation of the Hilbert transform in frequency domain, which approximation is based on a frequency main mode and one or more frequency twisted modes, wherein the frequency main and twisted modes carry, each, respective digital symbols to be transmitted.

TECHNICAL FIELD OF THE INVENTION

The present invention relates, in general, to a radio communicationssystem and method, namely a system and a method for implementingcommunications at Radio Frequency (RF) (including frequencies from a fewKHz to hundreds of GHz) with increased transmission capacity.

In particular, the present invention concerns a radio communicationssystem and method exploiting twisted signals in frequency domain forincreasing transmission capacity.

The present invention can be advantageously exploited, in general, inall kinds of radio communications, and, in particular, in radiocommunications based:

in general, on Orthogonal Frequency-Division Multiplexing (OFDM and/orOrthogonal Frequency-Division Multiple Access (OFDMA); and,

specifically, on Long Term Evolution (LTE) standard and/or WorldwideInteroperability for Microwave Access (WiMAX) standard.

BACKGROUND ART

In consideration of Orbital Angular Momentum (OAM) potentialities ofincreasing transmission capacity and since RF spectrum shortage problemis deeply felt in radio communications sector, recently a lot ofexperimental studies have been carried out on the use of OAM states, ormodes, at RF (also known as radio vortices) in order to try to enhanceRF spectrum reuse.

In this connection, reference may, for example, be made to:

Mohammadi S. M. et al., “Orbital Angular Momentum in Radio—A SystemStudy”, IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, IEEE SERVICECENTER, PISCATAWAY, N.J., US, vol. 58, no. 2, 1 Feb. 2010, pages565-572, which shows that standard antennas arranged in circular arrayscan be used to generate RF beams carrying OAM;

Tamburini F. et al., “Encoding many channels in the same frequencythrough radio Vorticity: first experimental test”, arXiv.org, 12 Jul.2011, Ithaca, N.Y., USA, which experimentally shows that it is possibleto propagate and use the properties of twisted non-monochromaticincoherent radio waves to simultaneously transmit several radio channelson one and the same frequency by encoding them in different (and,thence, orthogonal) OAM states (even without using polarization or densecoding techniques);

GB 2 410 130 A, which discloses a planar phased array antenna fortransmitting and receiving OAM radio vortex modes, which antennacomprises a circular array of cavity backed axial mode spiral antennaelements whose phase is controlled such that the phase of each antennaelement changes sequentially about the array; and

WO 2012/084039 A1, which discloses a transmit antenna arrangementcomprising N antenna elements arranged along a circumference with anangular separation of a degrees between neighboring antenna elements,the antenna arrangement comprising an OAM encoder arranged to receive Ninput signals for transmission, indexed from M=−(N−1)/2 up to M=(N−1)/2for odd N and from M=−(N−2)/2 up to N/2 for even N; the OAM encoderconnecting each input signal to each antenna element and giving eachinput signal M at each antenna element a phase shift of M*α relative tothe phase of the same input signal M at an adjacent antenna element;wherein two or more antenna elements are directional, have theirdirectivity in the same direction, and have an antenna aperture higherthan, or equal to, 5λ, where λ is the wavelength of the N input signals.

From a mathematical perspective, the transmission of an OAM mode (orstate) at a single RF (i.e., by using a pure tone) implies that theelectrical field on the radiating aperture can be represented as:

F(ρ,φ)=F(ρ)e ^(jkφ),

where ρ and φ are the cylindrical coordinates on the radiating aperture,j is the imaginary unit, and k is a positive or negative integer.

The radiated field can be represented in the far zone as:

${{E\left( {\vartheta,\phi} \right)} = {\frac{1}{R}{\int{\int_{S}{{F\left( {\rho,\varphi} \right)}^{{- {j2\pi}}\frac{\rho}{\lambda}{\sin {(\vartheta)}}{\cos {({\phi - \varphi})}}}\rho \ {\rho}{\varphi}}}}}},$

where θ and φ are the spherical coordinates in the far field, R denotesthe radius of the sphere centered on the radiating aperture, S denotesthe integration surface used at reception side, and λ denotes thewavelength used.

As is known, due to intrinsic characteristics of OAM, an OAM modetransmitted at a single RF (i.e., by using a pure tone) is affected by aphase singularity which creates a null at the bore-sight direction,thereby resulting that

E(0,0)=0.

In order for said phase singularity to be compensated, the integrationsurface S used at reception side should be sized so as to include thecrown peak generated by the OAM mode.

In particular, the integration surface S used at reception side shouldbe different for each OAM mode and, considering the sampling theoremapplied to the radiating antenna, should have an area given by:

${{\Delta \; S} = {{{\Delta\Omega}\; R^{2}} = {2\left( {\frac{\lambda}{D}R} \right)^{2}}}},$

where D denotes the diameter of the radiating antenna.

Therefore, the price to be paid with pure OAM modes transmitted by usingpure tones (i.e., single radiofrequencies) is that the dimensions of theequivalent receiving antenna depend on the distance R from, and on thediameter D of, the transmitting antenna.

This solution is impractical for satellite communications, where theaperture efficiency and the size of the antennas are very criticalissues. For example, in geostationary-satellite-based communications inKa band, for a ground antenna having a diameter D of about 9 m, thediameter of the receiving ring on board the geostationary satelliteshould be of the order of 50 Km, thereby resulting impractical.

Thence, in view of the foregoing, the main criticality in using radiovorticity in practical systems is that the orthogonality between OAMmodes depends on the size of antennas, on the distance between thetransmitting and receiving antennas, and on the need for the receivingantenna to operate as an interferometer basis (as, for example,disclosed in the aforesaid papers “Orbital Angular Momentum in Radio—ASystem Study” and “Encoding many channels in the same frequency throughradio Vorticity: first experimental test”, in GB 2 410 130 A and in WO2012/084039 A1). These constraints result in OAM-based radiocommunication systems which are inefficient and unusable for very longdistances such as the ones involved in satellite communications.

Moreover, further criticalities in the use of radio vorticity forsatellite communications are represented by the need of an extremelyaccurate mutual pointing of the transmitting and receiving antennas, andby the unfeasibility of the geometry for Earth-satellite configurationsdue to the criticality of the positioning of the receiving antennas (orthe receiving antenna elements).

A solution to the aforesaid technical problems is provided in theInternational Application No. PCT/IB2012/056804 filed on 28 Nov. 2012 inthe name of EUTELSAT S. A. and concerning a multidimensional spacemodulation technique for transmitting and/or receiving radio vortices atfrequencies ranging from a few KHz to hundreds of GHz. Specifically, themultidimensional space modulation technique according to theInternational Application PCT/IB2012/056804 allows to transmit and/orreceive orthogonal RF OAM modes in one and the same direction (i.e., thebore-sight direction) and to overcome, at the same time, the aforesaidtechnical problems caused by OAM phase singularity at the bore-sightdirection, thereby allowing the use of radio vortices also forlong-distance radio communications, such as satellite communications.

In particular, the multidimensional space modulation according to theInternational Application PCT/IB2012/056804 is actually a phasemodulation applied to signals to be transmitted at RF such that toresult in orthogonal radio vortices along the bore-sight direction.Therefore, the modulation according to the International ApplicationPCT/IB2012/056804 is called multidimensional space modulation because itallows orthogonal RF OAM modes to be transmitted and/or received in oneand the same direction, namely the bore-sight direction, wherein eachOAM mode represents a specific space channel along the bore-sightdirection, which specific space channel is orthogonal to all the otherspace channels represented by the other OAM modes.

In order for the multidimensional space modulation according to theInternational Application PCT/IB2012/056804 to be understood, attentionis drawn, by way of example, to the fact that, as is known, a twisted RFsignal having, or carrying, the OAM mode m=+1 is characterized by onlyone clockwise rotation of 360° of the Poynting vector around thepropagation axis per period T and, thence, it can be generated bytransmitting, for example by means of four ring-arranged transmittingantenna elements, RF signals associated with phases of 0°, 90°, 180°,and 270° clockwise distributed among said four ring-arrangedtransmitting antenna elements. Instead, the International ApplicationPCT/IB2012/056804 proves that it is possible and convenient, in order totransmit at RF the OAM mode m=+1 and, at the same time, to solve theproblem caused by OAM phase singularity at the bore-sight direction, toexploit only one antenna transmitting the four different phases 0°, 90°,180°, and 270° at different times (or at different frequencies) with atime step of T′=T/4. This possibility increases the efficiency of thetransmitting and receiving configuration, which can work regardless ofthe elementary antenna element spacing in an antenna array.

From a conceptual perspective, according to the InternationalApplication PCT/IB2012/056804, in order to manage OAM rotation, namelyin order to control the speed of rotation of an RF OAM mode about thebore-sight direction, a supplementary phase modulation is introduced,which leaves only a residue of the OAM twist and keeps the OAM signaturein a limited bandwidth. This residual rotation achieved by means of thesupplementary phase modulation allows a signal having a proper bandwidthto be orthogonal to another signal having a different rotation (multipleof the minimum one). Therefore, an RF twisted wave can be transmitted bymeans of a modulated waveform and can be received by an antennaoperating in the complex conjugate mode. The received signal is equal tothe transmitted one, apart from standard attenuation and transmissionand reception gains in a time period T_(mod). The bandwidth increasedoes not prevent the transmission of plane waves (i.e., the OAM modem=0), but limits the number of OAM modes at different centralfrequencies in the available bandwidth. The multidimensional spacemodulation according to PCT/IB2012/056804 allows to use a standardantenna in place of a phased array antenna, since the used signals arenative orthogonal.

It is important to underline the fact that the generation of RF OAMmodes by means of the multidimensional space modulation according toPCT/IB2012/056804 allows to drastically simplify the antenna design. Infact, the antenna does not need to take memory at the period of thecarrier frequency of the phase between elements f₀=1/T₀. This duty isperformed by the sampling frequency of the twisted waves, which is atleast 3 times the signal bandwidth; therefore the phase shift assignedto the sampling is already orthogonal in time; it follows that theantenna can be a standard one without the need of using a phased arrayconfiguration on either the antenna aperture, or, in case of a reflectorantenna, the focal plane. Therefore, the multidimensional spacemodulation according to PCT/IB2012/056804 can be exploited in satellitecommunications by using already existing satellite and ground antennas.

In order for the multidimensional space modulation according toPCT/IB2012/056804 to be better understood, reference is made to FIG. 1,which shows a functional block diagram of a transmitting system (denotedas whole by 1), which is disclosed in PCT/IB2012/056804 and whichexploits the aforesaid multidimensional space modulation fortransmitting radio vortices at frequencies ranging from a few KHz tohundreds of GHz.

In particular, the transmitting system 1 comprises:

a signal generation section 10 designed to generate

-   -   a first digital signal s₀(t) carrying an information stream,        having a given sampling period T₀ and occupying a given        frequency bandwidth W centered on a predefined frequency f₀, and    -   up to 2N second digital signals s_(m)(t), with −N≦m≦+N and N≧1        (for the sake of illustration simplicity in FIG. 1 only signals        s₊₁(t), s⁻¹(t), s_(+N)(t) and s_(31 N)(t) are shown), each        carrying a respective information stream, having a respective        sampling period T_(m)=4|m|T₀ (or T_(m)=3|m|T₀) and occupying a        respective frequency bandwidth W/4|m| (or W/3|m|) centered on        said predefined frequency f₀ (which can, conveniently, be an        Intermediate Frequency (IF) thereby resulting that the first and        second digital signals are IF digital signals);

a device 100 for generating OAM modes, which is coupled with said signalgeneration section 10 to receive the first and second digital signalsgenerated by the latter, and which is designed to

-   -   apply, to each second digital signal s_(m)(t) received from the        signal generation section 10, a respective space modulation        associated with a respective OAM mode m so as to generate a        corresponding modulated digital signal carrying said respective        OAM mode m, having the given sampling period T₀, and occupying        the given frequency bandwidth W, and    -   provide an output digital signal s_(out)(t) based on the        modulated digital signals and on the first digital signal s₀(t)        received from the signal generation section 10; and

an RF transmission section 1000, which is coupled with the device 100 toreceive therefrom the output digital signal s_(out)(t), and which isdesigned to transmit at predefined radio frequencies the output digitalsignal s_(out)(t) by means of a single antenna (which is not shown inFIG. 1 for the sake of illustration simplicity and which can be also areflector antenna with a single feed) or an antenna array (which is notshown in FIG. 1 for the sake of illustration simplicity and which can bealso a multi-feed reflector antenna), thereby transmitting an overall RFsignal carrying

-   -   said first digital signal s₀(t) by means of a plane wave, and    -   said second digital signals s_(m)(t), each by means of a        corresponding radio vortex having the respective OAM mode m.

The aforesaid predefined radio frequencies can conveniently range from afew KHz to hundreds of GHz depending on the specific application forwhich the overall transmitting system 1 is designed.

Conveniently, the signal generation section 10 can be a signalgeneration section of a transmitting system for satellite communications(such as a transmitting system of a feeder link Earth station, of asatellite, or of a ground apparatus for satellite communications), or ofa device for wireless communications, such as LTE-based communications.

Accordingly, the RF transmission section 1000 can conveniently be an RFtransmission section of a transmitting system for satellitecommunications (such as a transmitting system of a feeder link Earthstation, of a satellite, or of a ground apparatus for satellitecommunications), or of a device for wireless communications, such asLTE-based communications.

Additionally, FIG. 2 shows in greater detail the device 100 forgenerating OAM modes, which device 100 comprises 2N OAM mode generationmodules. In particular, FIG. 2 shows, for the sake of illustrationsimplicity, only:

an OAM mode generation module 110 for generating OAM mode m=+1;

an OAM mode generation module 120 for generating OAM mode m=−1;

an OAM mode generation module 130 for generating OAM mode m=+N; and

an OAM mode generation module 140 for generating OAM mode m=−N.

In detail, a generic OAM mode generation module for generating OAM modem is operable to apply to a respective second digital signal s_(m)(t)received from the signal generation section 10 a respective spacemodulation associated with said OAM mode m so as to generate acorresponding space-modulated digital signal sms_(m)(t) carrying saidOAM mode m, having the given sampling period T₀, and occupying the wholegiven frequency bandwidth W centered on said predefined frequency f₀.

More in detail, the generic OAM mode generation module for generatingthe OAM mode m is operable to:

receive a synchronization signal synch_(m) (not shown in FIG. 2 for thesake of illustration clarity) indicating the given sampling period T₀and, conveniently, also the sampling period T_(m) of the respectivesecond digital signal s_(m)(t) received from the signal generationsection 10; and

apply the respective space modulation to said respective digital signals_(m)(t) by

-   -   digitally interpolating said respective second digital signal        s_(m)(t) on the basis of the received synchronization signal        synch_(m) so as to generate a corresponding        digitally-interpolated signal having the given sampling period        T₀;    -   applying to the digitally-interpolated signal a respective        digital phase modulation associated with said OAM mode m such        that to generate a corresponding phase-modulated signal carrying        said OAM mode m with a predefined OAM mode rotation speed; and    -   digitally filtering the phase-modulated signal thereby obtaining        a filtered signal which represents the aforesaid space-modulated        digital signal sms_(m)(t).

For example, the OAM mode generation module 110 is convenientlyconfigured to:

receive, from the signal generation section 10, the second digitalsignal s₊₁(t) and a synchronization signal synch₊₁ indicating the givensampling period T₀ and, conveniently, also the sampling period T₊₁=4T₀(or T₊₁=3T₀) of the second digital signal s₊₁(t);

digitally interpolate the second digital signal s₊₁(t) by outputting,for each digital sample of said second digital signal s₊₁(t), fourcorresponding digital samples with time step (i.e., time distance) T₀,thereby generating a corresponding digitally-interpolated signal havingthe given sampling period T₀;

apply to each set of four digital samples obtained by means of thedigital interpolation digital phase shifts related to the OAM mode +1with the predefined OAM mode rotation speed (namely, digital phaseshifts related to phase values 0, π/2, π and 3π/2) so as to generate acorresponding set of four phase-shifted digital samples, whichcorresponding set of four phase-shifted digital samples carries said OAMmode +1 with the predefined OAM mode rotation speed;

digitally filter each set of four phase-shifted digital samples obtainedby means of the digital phase shifting so as to output a correspondingset of four filtered digital samples; and

combine the sets of four filtered digital samples obtained by means ofthe digital filtering into a single filtered signal which represents thespace-modulated digital signal sms₊₁(t).

Accordingly, the OAM mode generation module 120 is convenientlyconfigured to:

receive, from the signal generation section 10, the second digitalsignal s⁻¹(t) and a synchronization signal synch⁻¹ indicating the givensampling period T₀ and, conveniently, also the sampling period T⁻¹=4T₀(or T⁻¹=3T₀) of the second digital signal s⁻¹(t);

digitally interpolate the second digital signal s⁻¹(t) by outputting,for each digital sample of said second digital signal s⁻¹(t), fourcorresponding digital samples with time step (i.e., time distance) T₀,thereby generating a corresponding digitally-interpolated signal havingthe given sampling period T₀;

apply to each set of four digital samples obtained by means of thedigital interpolation digital phase shifts related to the OAM mode −1with the predefined OAM mode rotation speed (namely, digital phaseshifts related to phase values 0, 3π/2, π and π/2) so as to generate acorresponding set of four phase-shifted digital samples, whichcorresponding set of four phase-shifted digital samples carries said OAMmode −1 with the predefined OAM mode rotation speed;

digitally filter each set of four phase-shifted digital samples obtainedby means of the digital phase shifting so as to output a correspondingset of four filtered digital samples; and

combine the sets of four filtered digital samples obtained by means ofthe digital filtering into a single filtered signal which represents thespace-modulated digital signal sms⁻¹(t).

The OAM mode generation modules for generating higher-order OAM modes(i.e., with |m|>1) operate, mutatis mutandis, conceptually in the sameway as the OAM mode generation modules 110 and 120.

Moreover, again with reference to FIG. 2, the device 100 furthercomprises:

a combining module 150 operable to combine the first digital signals₀(t) received from the signal generation section 10 and all thespace-modulated digital signals sms_(m)(t) generated by the OAM modegeneration modules into a corresponding combined digital signals_(c)(t); and

a transmission filtering module 160, which is operable to digitallyfilter the combined digital signal s_(c)(t) by means of a predefinedtransmission filter such that to adjust the signal bandwidth to thebandwidth of transmission radio channel (i.e., the specific radiochannel used in transmission) so as to reduce Inter-Symbol Interference(ISI), thereby obtaining a corresponding output digital signals_(out)(t); wherein the transmission filtering module 160 is coupledwith the RF transmission section 1000 to provide the latter with theoutput digital signal s_(out)(t).

For example, in case of (free-space) satellite communications on a radiochannel having the given frequency bandwidth W, the transmission filtercan be a predefined root raised cosine filter adapted to said givenfrequency bandwidth W.

As far as reception is concerned, reference is made to FIG. 3, whichshows a functional block diagram of a receiving system (denoted as wholeby 2), which is disclosed in PCT/IB2012/056804 and which exploits theaforesaid multidimensional space modulation for receiving radio vorticesat frequencies ranging from a few KHz to hundreds of GHz.

In particular, the receiving system 2 comprises:

an RF reception section 2000, which is designed to receive signals atpredefined radio frequencies by means of a single antenna (which is notshown in FIG. 3 for the sake of illustration simplicity and which can bealso a reflector antenna with a single feed) or an antenna array (whichis not shown in FIG. 3 for the sake of illustration simplicity and whichcan be also a multi-feed reflector antenna), and which is designed toobtain an incoming digital signal u_(in)(t) on the basis of the receivedsignals;

a device 200 for demodulating OAM modes, which is coupled with said RFreception section 2000 to receive the incoming digital signal u_(in)(t)therefrom, and which is designed to process said incoming digital signalu_(in)(t) so as to output useful signals (in FIG. 3 useful signalsu₀(t), u₊₁(t), u⁻¹(t), u_(+N)(t) and u_(−N)(t) outputted by the device200 are shown); and

a signal processing section 20, which is coupled with said device 200 toreceive the useful signals outputted by the latter and which is designedto process said useful signals.

The aforesaid predefined radio frequencies can conveniently range from afew KHz to hundreds of GHz depending on the specific application forwhich the overall receiving system 2 is designed.

Conveniently, the RF reception section 2000 can be an RF receptionsection of a receiving system for satellite communications (such as areceiving system of a feeder link Earth station, of a satellite, or of aground apparatus for satellite communications), of a device for wirelesscommunications (such as LTE-based communications), of a radar system, ofa Synthetic Aperture Radar (SAR) system, or of a radio astronomyreceiving system.

Accordingly, the signal processing section 20 can conveniently be asignal processing section of a receiving system for satellitecommunications (such as a receiving system of a feeder link Earthstation, of a satellite, or of a ground apparatus for satellitecommunications), of a device for wireless communications (such asLTE-based communications), of a radar system, of a SAR system, or of aradio astronomy receiving system.

Additionally, FIG. 4 shows in greater detail the device 200 fordemodulating CAM modes. In particular, as shown in FIG. 4, the device200 comprises a reception filtering module 210, which is operable todigitally filter the incoming digital signal u_(in)(t) by means of apredefined reception filter such that to equalize the incoming digitalsignal u_(in)(t) with respect to reception radio channel (i.e., thespecific radio channel used in reception) and, conveniently, also withrespect to transmission filter (i.e., the specific filter used intransmission), thereby obtaining a corresponding filtered incomingdigital signal u_(f)(t).

For example, in case of (free-space) satellite communications on a radiochannel having the given frequency bandwidth W, wherein the transmissionfilter is a predefined root raised cosine filter adapted to said givenfrequency bandwidth W, the reception filter can be the complex conjugateof said predefined root raised cosine filter so as to reduce ISI.

Additionally, again with reference to FIG. 4, the device 200 furthercomprises a digital oversampling module 220 operable to digitallyoversample the filtered incoming digital signal u_(f)(t) on the basis ofa predefined oversampling period T_(over), thereby outputting acorresponding set of digital samples.

For example, in case the receiving system 2 is configured to receive theRF signals transmitted by the transmission system 1, the predefinedoversampling period T_(over) can conveniently be equal to T₀/Q, whereinT₀ is the given sampling period previously introduced in connection withthe transmission system 1, and Q denotes an integer higher than one.

Furthermore, again with reference to FIG. 4, the device 200 comprisesalso a processing module 230 configured to:

provide a linear system of M equations (where M denotes an integerhigher than one) relating

-   -   the set of digital samples outputted by the digital oversampling        module 220    -   to X unknown digital values (where X denotes an integer higher        than one and lower than M) of useful signals associated, each,        with a respective predefined OAM mode m with a predefined OAM        mode rotation speed;    -   wherein said linear system of M equations relates the set of        digital samples outputted by the digital oversampling module 220        to the X unknown digital values through        -   first predefined parameters related to the predefined OAM            modes with the predefined OAM mode rotation speed, and        -   second predefined parameters related to the predefined            reception filter, to the reception radio channel and,            conveniently, also to the transmission filter;

compute the X digital values by solving the linear system of Mequations; and

digitally generate and output the useful signals (for example the usefulsignals u₀(t), u₊₁(t), u⁻¹(t), u_(+N)(t) and u_(−N)(t) shown in FIG. 4)on the basis of the corresponding digital values computed.

In this connection, it is important to underline the fact that, in orderto extract the useful signals (i.e., in order to solve the linear systemof M equations thereby computing the X digital values, and, thence, togenerate and output the useful signals), the processing module 230 isconveniently configured to operate as a generalized matched filter whichexploits one or more mathematical processing techniques, such as thepseudo-inverse technique.

Moreover, it is also important to underline the fact that theoversampling operation performed by the digital oversampling module 220allows to increase redundancy of the linear system of M equations (i.e.,it allows to obtain a number M of independent equations higher andhigher than the number X of the unknown digital values), therebyallowing to find more robust solutions to said linear system of Mequations.

Furthermore, the better the characterization of the OAM modes and of theradio channel in the linear system of M equations, the more robust theresolution of said linear system of M equations. Specifically, anincrease of the number of first and second predefined parameters used inthe linear system of M equations allows to increase redundancy of saidlinear system of M equations (i.e., it allows to obtain a number M ofindependent equations higher and higher than the number X of the unknowndigital values), thereby allowing to optimize the resolution of, i.e.,to find optimum solutions to, said linear system of M equations in termsof energy per bit to noise power spectral density ratio E_(b)/N₀.

In case the receiving system 2 is configured to receive the RF signalstransmitted by the transmission system 1, the first predefinedparameters are related to the sampling periods T₀ and T_(m) previouslyintroduced in connection with the device 100, and to the digital phaseshifts applied by the OAM mode generation modules of the device 100 tothe digital samples of the digitally-interpolated signals.

Moreover, again in case the receiving system 2 is configured to receivethe RF signals transmitted by the transmission system 1, the usefulsignals generated and outputted by the processing module 230 (such asthe signals u₀(t), u₊₁(t), u⁻¹(t), u_(+N)(t) and u_(−N)(t) shown in FIG.4) are the digital signals transmitted by said transmission system 1 bymeans of the plane wave and the several radio vortices (namely thesignals s₀(t), s₊₁(t), s⁻¹(t), s_(+N)(t) and s_(−N)(t) shown in FIGS. 1and 2).

Preferably, the device 100 for generating OAM modes and the device 200for demodulating OAM modes are implemented by means ofField-Programmable Gate Array (FPGA), Application-Specific IntegratedCircuit (ASIC), and Software Defined Radio (SDR) technologies.

Finally, according to a further aspect of to the InternationalApplication PCT/IB2012/056804, an overall radio communication systemincluding both the transmission system 1 and the receiving system 2 ispreferably designed to:

monitor interference experienced by the radio vortices transmitted; and,

if the interference experienced by a radio vortex carrying a givendigital signal s_(m)(t) by means of a given OAM mode m meets a giveninterference-related condition (for example, if it exceeds a giveninterference level),

-   -   start using an OAM mode m* different from the given OAM mode m        for transmitting the information stream previously carried by        said given digital signal s_(m)(t) by means of said given OAM        mode m, and    -   stop using said given OAM mode m.

In case said further aspect of PCT/IB2012/056804 is used for satellitecommunications, it is possible to mitigate jammer, since said furtheraspect of PCT/IB2012/056804 allows to reject a jammed OAM mode.Moreover, said further aspect of PCT/IB2012/056804 can be used also incombination with other anti-jamming capabilities of the receivingsystem.

OBJECT AND SUMMARY OF THE INVENTION

The Applicant has carried out an in-depth study in order to develop apractical, efficient mode for carrying out the multidimensional spacemodulation disclosed in the International Application PCT/IB2012/056804,and this in-depth study has led the Applicant to develop a new,inventive system and method for transmitting and receiving signals atRadio Frequency (RF) (including frequencies from a few KHz to hundredsof GHz) with increased transmission capacity.

Therefore, an object of the present invention is that of providing asystem and a method for transmitting and receiving RF signals withincreased transmission capacity.

This and other objects are achieved by the present invention in so faras it relates to a method and a system for radio communications, asdefined in the appended claims.

In particular, the radio communications method according to the presentinvention comprises carrying out, by a transmitter, the following steps:

a) providing a digital time signal carrying digital symbols to betransmitted; and

b) transmitting a radio frequency signal carrying said digital timesignal.

Moreover, the method according to the present invention furthercomprises carrying out, by a receiver, the following steps:

c) receiving the radio frequency signal transmitted by the transmitter;

d) processing the received radio frequency signal so as to obtain acorresponding incoming digital signal; and

e) extracting, from the incoming digital signal, the digital symbolscarried by said incoming digital signal.

The method according to the present invention is characterized in thatsaid digital time signal carrying the digital symbols to be transmittedresults from an approximation of the Hilbert transform in frequencydomain, which approximation is based on a frequency main mode and one ormore frequency twisted modes, wherein said frequency main and twistedmodes carry, each, respective digital symbols to be transmitted.

Conveniently, the digital time signal is time-limited, carries a limitedsequence of digital symbols to be transmitted, and results from:

main mode frequency samples carrying respective digital symbols of saidlimited sequence via a frequency main mode; and

twisted mode frequency samples carrying the other digital symbols ofsaid limited sequence via one or more frequency twisted modes, whereineach frequency twisted mode is a complex harmonic mode that isorthogonal to the frequency main mode and to any other frequency twistedmode used.

More conveniently, the main mode frequency samples are at main modefrequencies spaced apart by a predetermined frequency spacing, and thetwisted mode frequency samples comprise, for a frequency twisted mode,respective twisted mode frequency samples at corresponding twisted modefrequencies that:

are related to said frequency twisted mode;

are spaced apart by said predetermined frequency spacing; and

are different from the main mode frequencies.

More and more conveniently, the one or more frequency twisted modescomprise 2N frequency twisted modes each identified by a respectiveinteger index n that is comprised between −N and +N and is differentfrom zero, N denoting an integer higher than zero; the limited sequenceof digital symbols to be transmitted comprises S_(TOT) digital symbols,S_(TOT) being equal to 2^(N+2)−1; the frequency main mode carriesM_(MFS) of said S_(TOT) digital symbols by means of M_(MFS) main modefrequency samples at corresponding main mode frequencies, that arespaced apart by said predetermined frequency spacing and that range fromB_(S) to M_(MFS) times B_(S), B_(S) denoting said predeterminedfrequency spacing and M_(MFS) being equal to 2^(N+1)+1; said 2Nfrequency twisted modes carry the S_(TOT)−M_(MFS) digital symbols notcarried by the frequency main mode; and each frequency twisted mode ncarries 2_(N−|n|) respective digital symbol(s) by means of 2^(N+1)respective twisted mode frequency samples at corresponding twisted modefrequencies, that are spaced apart by said predetermined frequencyspacing and that are located, in frequency domain, at

${B_{S}\left( {\frac{2^{n} - 1}{2^{n}} + k} \right)},$

where k denotes an integer ranging from zero to 2^(N+1)−1, or from oneto 2^(N+1).

Very conveniently, each of said _(STOT) digital symbols to betransmitted is represented by a respective symbol complex value; and,for each frequency twisted mode n, the 2_(N+1) respective twisted modefrequency samples comprise, for each of the 2^(N−|n|) respective digitalsymbol(s), 2^(|n|+1) frequency samples, that:

carry said digital symbol;

are at frequencies that are located, in frequency domain, at

${B_{S}\left\lbrack {\frac{2^{n} - 1}{2^{n}} + \left( {k^{*} + {i \cdot 2^{{n} + 1}}} \right)} \right\rbrack},$

where k* denotes an integer ranging from zero to 2^(|n|+1)−1, or fromone to 2^(|n|+1), and where i is an index that identifies said digitalsymbol and is comprised between zero and 2^(N−|n|)−1; and

have, each, a respective complex value obtained by multiplying thesymbol complex value representing said digital symbol by a respectivecomplex factor related to said frequency twisted mode n and to thefrequency of said frequency sample.

Again very conveniently, for each frequency twisted mode n and for eachof the 2^(N−|n|) respective digital symbol(s), the 2^(|n|+1) respectivefrequency samples carrying said digital symbol have, each, a respectivecomplex value obtained by multiplying the symbol complex valuerepresenting said digital symbol by a respective complex factor which:

if n is higher than zero, is equal to

$\frac{^{{+ j}\; k^{*}\frac{\pi}{2^{n}}}}{2^{\frac{{n} + 1}{2}}}$

or, if n is lower than zero, is equal to

$\frac{^{{- j}\; k^{*}\frac{\pi}{2^{n}}}}{2^{\frac{\;^{n}{+ 1}}{2}}}$

where j denotes the imaginary unit.

Preferably, said step a) includes providing the digital time signal byusing a predefined transmission matrix that relates

the S_(TOT) digital symbols to be transmitted

to time samples of the digital time signal

through coefficients related to a transform from frequency domain totime domain of the main mode frequency samples and the twisted modefrequency samples;

and said step e) includes extracting the digital symbols carried by theincoming digital signal by using a reception matrix derived from thepredefined transmission matrix (conveniently, through a pseudo-inversetechnique).

Preferably, the main mode frequency samples are frequency samples ofOrthogonal Frequency-Division Multiplexing (OFDM) type, or of OrthogonalFrequency-Division Multiple Access (OFDMA) type.

Preferably, said step a) includes:

providing a first digital time signal resulting from the main modefrequency samples and the twisted mode frequency samples; and

providing a second digital time signal which includes a cyclic prefixfollowed by the first digital time signal, wherein the cyclic prefix isa replica of an end portion of said first digital time signal;

and said step b) includes transmitting a radio frequency signal carryingthe second digital time signal.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the present invention, preferredembodiments, which are intended purely by way of non-limiting example,will now be described with reference to the attached drawings (all notto scale), wherein:

FIG. 1 schematically illustrates a transmitting system for transmittingradio vortices according to the background art;

FIG. 2 schematically illustrates a device for generating OAM modes,which device is exploited by the transmitting system shown in FIG. 1;

FIG. 3 schematically illustrates a receiving system for receiving radiovortices according to the background art;

FIG. 4 schematically illustrates a device for demodulating OAM modes,which device is exploited by the receiving system shown in FIG. 2;

FIG. 5 schematically illustrates time behavior of a complex frequencyfunction constituted by a real cosinusoidal function and an imaginarysinusoidal function;

FIGS. 6 and 7 schematically illustrate complex frequency samples of asignal limited in time and of its corresponding analytical signal,respectively (assuming that the signal can be approximated as aband-limited signal too);

FIGS. 8 and 9 schematically illustrate time inverse Fourier transform ofa complex frequency function and time inverse Fourier transform of itsfrequency Hilbert transform, respectively;

FIG. 10 schematically illustrates a comparison between a process forgenerating twisted waves in time domain according to Internationalapplication PCT/FR2013/052636, and a process for generating twistedwaves in frequency domain according to the present invention;

FIGS. 11 and 12 schematically illustrate a complex frequency function ofan analytical signal and its Hilbert transform in frequency domain,respectively;

FIG. 13 schematically illustrates frequency Hilbert transform andapproximations of the latter obtained by using, respectively, one, two,and five orthogonal exponential modes;

FIGS. 14, 15 and 16 schematically illustrate frequency behavior of threedifferent orthogonal exponential modes;

FIG. 17 schematically illustrates powers associated with orthogonalharmonic modes used to develop frequency Hilbert transform;

FIGS. 18 and 19 schematically illustrate frequency twist complexfunctions related to two orthogonal harmonic modes;

FIG. 20 schematically illustrates an OFDM super frame with additionalTwisted frame Frequency Units (TFUs);

FIG. 21 schematically illustrates an approximation of the impulseresponse of the frequency Hilbert transform using three complex harmonicmodes;

FIG. 22 schematically represents a radio communications method accordingto the present invention as a generalization of the traditional OFDM (orOFDMA) technique;

FIGS. 23 and 24 schematically illustrate time behavior of a time twistedmode +1 complex signal and of a frequency twisted mode +1 complexsignal, respectively;

FIGS. 25 and 26 schematically illustrate symbol and clock timerelationship according to an aspect of the present invention;

FIG. 27 schematically illustrates a traditional scheme of cyclic prefixfor OFDM-OFDMA;

FIG. 28 schematically illustrates an example of two delay spreadcomponents with cyclic prefix;

FIG. 29 schematically illustrates time frame duration increase due tocyclic prefix;

FIGS. 30 and 31 schematically illustrate time behavior of main mode andtwisted modes, respectively, when a cyclic prefix is used;

FIG. 32 schematically illustrates noise bandwidths for time twistedwaves;

FIG. 33 schematically illustrates noise impact in the case of frequencytwisted waves;

FIG. 34 schematically illustrates spectral efficiency as a function ofthe energy per symbol over noise density for frequency twisted waves;

FIG. 35 schematically illustrates a frequency structure of frequencytwisted waves according to an illustrative embodiment of the presentinvention;

FIG. 36 schematically illustrates a transmitting system according to anillustrative embodiment of the present invention;

FIG. 37 schematically illustrates a receiving system according to anillustrative embodiment of the present invention;

FIG. 38 schematically illustrates an example of square matrix resultingfrom the multiplication of the transpose of a transmission matrixaccording to an aspect of the present invention by said transmissionmatrix;

FIG. 39 schematically illustrates a multilayer architecture wherein aframe structure of frequency twisted waves according to an aspect of thepresent invention is embedded in a traditional OFDM architecture;

FIG. 40 schematically illustrates computational complexity of thepresent invention and frequency reuse according to the present inventionas a function of the number of frequency twisted modes used; and

FIG. 41 schematically illustrates flexibility in using OFDM modularity,complex equation number and implementation criticality of the presentinvention as a function of the number of frequency twisted modes used.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION

The following discussion is presented to enable a person skilled in theart to make and use the invention. Various modifications to theembodiments will be readily apparent to those skilled in the art,without departing from the scope of the present invention as claimed.Thus, the present invention is not intended to be limited to theembodiments shown and described, but is to be accorded the widest scopeconsistent with the principles and features disclosed herein and definedin the appended claims.

The present invention relates to a practical, efficient mode, ingeneral, for increasing transmission capacity and, in particular, forincreasing RF spectrum reuse. In this connection, InternationalApplication No. PCT/FR2013/052636 (whose content is herewith enclosed byreference) filed on 5 Nov. 2013 in the name of EUTELSAT S. A. disclosesthe feasibility of increasing transmission capacity at Radio Frequency(RF) (including frequencies from a few KHz to hundreds of GHz) byexploiting a proper approximation in time domain of the Hilberttransform of digital analytical signals, wherein said approximation ofthe Hilbert transform is implemented by using twisted waves,specifically orthogonal harmonic modes.

In particular, PCT/FR2013/052636 describes a radio communicationssystem, which comprises a transmitter and a receiver, wherein thetransmitter is configured to:

generate or receive digital symbols having a given symbol rateassociated with a corresponding symbol period;

generate, every S digital symbols generated/received, a respectivemulti-mode digital signal, which has a predefined time length shorterthan S times the symbol period, which is sampled with a predefinedsampling rate higher than the symbol rate, and which carries said Sdigital symbols by means of a plurality of orthogonal harmonic modescomprising

-   -   a main mode which is a real harmonic mode and carries P of said        S digital symbols, and    -   one or more secondary modes carrying the other S-P digital        symbols, each secondary mode being a complex harmonic mode        time-shifted by half the symbol period with respect to the main        mode (wherein S is an integer higher than three and P is an        integer lower than S); and

transmit a radio frequency signal carrying a sequence of the generatedmulti-mode digital signals.

Moreover, the receiver of the radio communications system according toPCT/FR2013/052636 is configured to:

receive the radio frequency signal transmitted by the transmitter;

process the received radio frequency signal so as to obtain acorresponding incoming digital signal; and

extract, from successive, non-overlapped portions of the incomingdigital signal sampled with the predefined sampling rate, the S digitalsymbols respectively carried by each incoming digital signal portion bymeans of the orthogonal harmonic modes; wherein each of the successive,non-overlapped portions of the incoming digital signal has thepredefined time length.

Preferably, the transmitter according to PCT/FR2013/052636 is configuredto generate a multi-mode digital signal carrying S digital symbols by:

allocating P of the S digital symbols to the main mode by providing, foreach of said P digital symbols, a corresponding complex value whichrepresents said digital symbol and is related to the main mode;

allocating each of the other S-P digital symbols to a correspondingsecondary mode by providing, for each of said S-P digital symbols, acorresponding complex value which represents said digital symbol and isrelated to the secondary mode to which said digital symbol is allocated;

computing, by using a predefined transmission matrix, M multi-modecomplex values related to M successive time instants which, within thepredefined time length, are separated by half the symbol period, whereinM is an integer equal to or higher than S, and wherein the predefinedtransmission matrix relates

-   -   the S complex values representing the S digital symbols and        related to the harmonic modes    -   to the M successive time instants    -   through complex coefficients each of which is related to a        respective harmonic mode and to a respective time instant; and

generating a multi-mode digital signal having the predefined time lengthand sampled with the predefined sampling rate on the basis of the Mmulti-mode complex values computed.

Again preferably, the receiver according to PCT/FR2013/052636 isconfigured to extract the S digital symbols carried by an incomingdigital signal portion having the predefined time length and sampledwith the predefined sampling rate by:

extracting, from said incoming digital signal portion, M multi-modecomplex values related to M successive time instants which are, withinthe predefined time length, separated by half the symbol period;

computing, by using a reception matrix derived from the predefinedtransmission matrix, S complex values representing the S digital symbolcarried by said incoming digital signal portion by means of theorthogonal harmonic modes, wherein said reception matrix relates

-   -   the M extracted multi-mode complex values related to the M        successive time instants    -   to the S complex values to be computed    -   through complex coefficients each of which is related to a        respective harmonic mode and to a respective time instant; and

determining the S digital symbols represented by the S complex valuescomputed.

Conveniently, the reception matrix used by the receiver according toPCT/FR2013/052636 is derived from the predefined transmission matrixthrough a generalized inversion technique.

More conveniently, according to PCT/FR2013/052636, the predefinedtransmission matrix is such that the matrix resulting from themultiplication of the transpose of said predefined transmission matrixand said predefined transmission matrix has a determinant different fromzero, and the reception matrix is derived from the predefinedtransmission matrix through a pseudo-inverse technique.

More and more conveniently, according to PCT/FR2013/052636, thereception matrix is computed on the basis of the following formula:

[[GMF]]=([[A]] ^(T) [[A]])⁻¹ [[A]] ^(T),

where [[GMF]] denotes the reception matrix, [[A]] dentoes the predefinedtransmission matrix, [[A]]^(T) dentoes the transpose of the predefinedtransmission matrix, and ([[A]]^(T) [[A]])⁻¹ denotes the operation ofinversion of the matrix resulting from the multiplication of thetranspose of the predefined transmission matrix and the predefinedtransmission matrix.

Preferably, according to PCT/FR2013/052636, the main mode comprises,within the predefined time length, P samples with sampling period equalto the symbol period, the secondary modes comprise, within thepredefined time length, P−1 samples with sampling period equal to thesymbol period, each secondary mode is time-shifted by half the symbolperiod with respect to the main mode, and said M successive timeinstants, which, within the predefined time length, are separated byhalf the symbol period, are the sampling times of the main mode and ofthe secondary modes, thereby resulting that M=2P−1.

More preferably, according to PCT/FR2013/052636, the harmonic modescomprise 2N secondary complex harmonic modes each of which carries arespective Orbital Angular Momentum (OAM) mode and has a respectivetopological-charge-related index n comprised between −N and +N, whereinN is an integer higher than one; moreover, the main mode carriesP=2^(N+1)+1 digital symbols and each secondary complex harmonic modehaving topological-charge-related index n carries 2^(N−n+1) digitalsymbols, thereby resulting that M=2^(N+2)+1 and S=2^(N+2)−1.

Conveniently, according to PCT/FR2013/052636, the predefined samplingrate depends at least on the predefined time length of each multi-modedigital signal and of each of the successive, non-overlapped portions ofthe incoming digital signal.

More conveniently, according to PCT/FR2013/052636, the predefined timelength is equal to P times the symbol period.

More and more conveniently, according to PCT/FR2013/052636, thepredefined sampling rate is determined on the basis of the followinaformula:

${{CR} = {\frac{{2\; P} + u}{2\; P} \cdot \frac{1}{T_{S}}}},$

where CR denotes said predefined sampling rate, T_(s) denotes the symbolperiod, and u denotes a digital-vestigial-component-related parameterwhose value is an integer and depends at least on the predefined timelength.

Preferably, the transmitter according to PCT/FR2013/052636 is configuredto generate a multi-frame digital signal comprising successive,non-overlapped time frames each of which has the predefined time lengthand is occupied by a respective multi-mode digital signal; moreover, themulti-frame digital signal carries frame synchronization data related toframe synchronization of its time frames; accordingly, the radiofrequency signal transmitted by the transmitter carries the multi-framedigital signal.

Additionally, the receiver according to PCT/FR2013/052636 is furtherconfigured to:

extract the frame synchronization data from the incoming digital signal;

detect, on the basis of the extracted frame synchronization data,successive, non-overlapped time frames of the incoming digital signalwith the predefined time length; and,

for each detected time frame of the incoming digital signal, extract,from the incoming digital signal portion within said time frame, the Sdigital symbols carried by said incoming digital signal portion by meansof the orthogonal harmonic modes.

More preferably, according to PCT/FR2013/052636, the multi-frame digitalsignal comprises a preamble followed by F successive, non-overlappedtime frames occupied, each, by a respective multi-mode digital signal, Fbeing an integer higher than one; in particular, the preamble carriesframe synchronization data related to frame synchronization of the Ffollowing time frames.

More and more preferably, according to PCT/FR2013/052636, the framesynchronization data indicate time frame beginning and/or the predefinedtime length of the time frames.

In order to increase, in general, transmission capacity at RadioFrequency (RF) (including frequencies from a few KHz to hundreds of GHz)and, in particular, RF spectrum reuse, the present invention, byexploiting duality between time and frequency, teaches to use atwisted-wave-based approximation of the Hilbert transform in frequencydomain.

In particular, thanks to duality principle between time and frequency itis possible to exploit twisted wave functions also in frequency domain.The results are very interesting and promising with features which are,on the one hand, similar to time domain case, but, on the other hand,rather different, for practical applications, from time domain case.

In detail, “frequency twist” can be seen as a generalisation of thewell-known OFDM approach, introducing an absolute novelty in theanalysis and design of OFDM signals.

Theory underlying the present invention will be presented in thefollowing.

As is known, a signal can be represented in time or frequency domain,time and frequency being conjugate variables.

Considering a time-limited signal within a time window T (as usualtechnique in the case of OFDM-OFDMA signals), in frequency domain saidsignal can be represented by a series of sinc functions:

${X(f)} = {\sum\limits_{k = {- \infty}}^{+ \infty}\; {a_{k}^{{j\phi}_{k}}{\frac{\sin \left\lbrack {\pi \; {T\left( {f - \frac{k}{T}} \right)}} \right\rbrack}{\pi \; {T\left( {f - \frac{k}{T}} \right)}}.}}}$

In the case the signal X(f) can be approximated with a band-limitedsignal with bandwidth B, this implies that:

X(f−f ₀)=X ⁺(f−f ₀)+X ⁻(f−f ₀),

where + and − denote positive and negative frequencies, respectively.

Taking into consideration only the positive frequencies, it is possibleto write:

X ⁺(f−f ₀)=X(f−f ₀) for f≧0, and

X ⁺(f−f ₀)=0 for f <0,

and also

${{X^{+}(f)} = {\sum\limits_{k = {- N}}^{+ N}\; {a_{k}^{{j\phi}_{k}}\frac{\sin \left\lbrack {\pi \; {T\left( {f - f_{0} - \frac{k}{T}} \right)}} \right\rbrack}{\pi \; {t\left( {f - f_{0} - \frac{k}{T}} \right)}}}}},$

where N=TB.

Thence, each sample is constituted by a real part given by a_(k) cosφ_(k), and an imaginary part given by a_(k) sin φ_(k). The timerepresentation of such a sample is given by one cosinusoidal function inthe time window T, having an amplitude of a_(k) cos φ_(k), and onesinusoidal function having an amplitude of a_(k) sin φ_(k), as shown inFIG. 5 where time behavior of said complex frequency sample isillustrated.

The frequency pattern is given by two couples of sinc functions, namelyone for the real part and one for the imaginary part, as shown in FIGS.6 and 7 which illustrate complex frequency samples of a signal limitedin time and of its corresponding analytical signal, respectively(assuming that the signal can be approximated as a band-limited signaltoo).

As far as analytical signals are concerned, the traditional Hilberttransform is applied in time, assuming that the total bandwidth of thesignal can be considered limited and that the baseband signal has beenshifted to a proper frequency such that to allow the full bandwidth tobe on the positive frequency semiaxis (and, of course, replicated on thenegative one). On the positive frequency semiaxis, with respect to thecentral frequency sample for k=0, frequency samples are complex andthere results that a_(k)e^(jφ) ^(k) ≠a_(31 k)e^(jφ) ^(−k) .

Taking into consideration a complex frequency sample related to alimited time window, it is possible to apply a second Hilbert transformto the function X⁺(f−f₀) in frequency domain (on the assumption that thesignal is a limited time duration signal):

${{X_{H}^{+}\left( {f - f_{0}} \right)} = {\int_{- \infty}^{+ \infty}{\frac{X(\phi)}{\pi \left( {f - f_{0} - \phi} \right)}\ {\phi}}}},$

where the integral can be understood as the main Cauchy value.

Thence, the time function results to be:

x _(H)(t)=x(t)e ^(j2πf) ⁰ ^(t)(u ₀(t)−u ₀(−t)),

where u₀(t) and u₀(−t) are the step functions for t>0 and t<0,respectively.

On the assumption that

${\left. {X(f)} \right|_{f_{k} = \frac{k}{T}} = \frac{\sin \left\lbrack {\pi \left( {{fT} - k} \right)} \right\rbrack}{\pi \left( {{fT} - k} \right)}},$

then the time function is given by:

$\begin{matrix}{{{x(t)} = ^{{j2\pi}\mspace{11mu} k\frac{t}{T}}},} & {{{{for}\mspace{14mu} {t}} < \frac{T}{2}},{and}} \\{{{x(t)} = 0},} & {{{for}\mspace{14mu} {t}} \geq {\frac{T}{2}.}}\end{matrix}$

Thence, the time transform of the frequency Hilbert transform results tobe:

$\begin{matrix}{{{x(t)}\left( {{u_{0}(t)} - {u_{0}\left( {- t} \right)}} \right)} = ^{{j2\pi}\; k\frac{t}{T}}} & {{{{for}\mspace{14mu} 0} < t < \frac{T}{2}},} \\{{{x(t)}\left( {{u_{0}(t)} - {u_{0}\left( {- t} \right)}} \right)} = {- ^{{j2\pi}\; k\frac{t}{T}}}} & {{{{for}\mspace{14mu} - \frac{T}{2}} < t < 0},{and}} \\{{{x(t)}\left( {{u_{0}(t)} - {u_{0}\left( {- t} \right)}} \right)} = 0} & {{{for}\mspace{14mu} {t}} \geq \frac{T}{2}}\end{matrix}.$

In this respect, FIGS. 8 and 9 show time inverse Fourier transform of acomplex frequency function and time inverse Fourier transform of itsfrequency Hilbert transform, respectively.

The analysis of properties of this signal family is thence based on asequential application of one time Hilbert transform to get theanalytical signal and one frequency Hilbert transform to get the twistedwave signals, which are orthogonal to the original samples.

The process just described is similar but somewhat substantiallydifferent from time twist case. In fact, as described inPCT/FR2013/052636, in time twist the Hilbert transform is applied twicein time: the first time Hilbert transform is used to get the analyticalsignal, and the second time Hilbert transform is used to create thefamily of twisted waves orthogonal to the original samples.

In this respect, FIG. 10 schematically shows a comparison of theprocesses for generating twisted waves in time domain according toPCT/FR2013/052636 and in frequency domain according to the presentinvention.

In particular, as shown in FIG. 10, both the process according toPCT/FR2013/052636 (denoted as a whole by 300) and the process accordingto the present invention (denoted as a whole by 400) are applied to alimited-band signal x(t) and include:

applying to the limited-band signal x(t) a frequency shift (block 301and 401, respectively); and

performing a time Hilbert transform of the frequency-shifted signal toget the analytical signal (block 302 and 402, respectively).

Instead, the two processes are differentiated by the fact that:

the process 300 according to PCT/FR2013/052636 exploits an approximationin time domain of the Hilbert transform of the analytical signal tocreate time twisted waves (block 303); and

the process 400 according to the present invention exploits anapproximation in frequency domain of the Hilbert transform of theanalytical signal to create frequency twisted waves (block 403).

In detail, as far as the process 400 according to the present inventionis concerned, the Hilbert transform in frequency domain can be seen asan inverse Fourier transform of the analytical signal previouslydescribed. In this respect, FIGS. 11 and 12 show complex frequencyfunction of the analytical signal and its Hilbert transform in frequencydomain, respectively.

The frequency Hilbert transform increases the bandwidth necessary torepresent the signal, due to the presence of a discontinuity in the timefunction at the origin (i.e., taking into consideration the meaning ofthe main Cauchy value, the position of the symmetry/asymmetry axis ofthe integration). This aspect is similar to the situation of the Hilberttransform in time domain, and can be handled by considering adevelopment into a series of orthogonal modes. In this respect, FIG. 13shows frequency Hilbert transform and approximations of the latterobtained by using, respectively, one, two, and five orthogonalexponential modes.

Each mode higher than mode 0 is represented by a couple of odd pulses infrequency domain, centered with respect to the frequency f₀. In thisrespect, FIGS. 14, 15 and 16 show frequency behavior of the mode 0, 1and 2, respectively. The modes are mutually orthogonal, but theorthogonality between each of them and the main mode frequency pulses isgiven by the symmetry property of the full bandwidth and this could bedefined as a synoptic orthogonality.

Similarly to the time domain case, the above property is similar tointerferometry, which is a property depending on the space geometry andnot directly on the signal.

Therefore, frequency domain can be assimilated to a sort of space(specifically, a “frequency space”), similarly to the situation of thetime twist where the time is considered a space (specifically, a “timespace”), with additional degrees of freedom.

It is important to note a basic difference between time and thefrequency pulses: time pulses are real, while frequency pulses are ingeneral complex.

Therefore, the frequency twist shows a more robust capability to carryan additional information channel. In fact, while for time twist it isnecessary to increase the nominal Nyquist bandwidth (approximately of33%), the frequency twist can work without this limitation.

The frequency Hilbert transform allows, theoretically, to maintain allthe information content of the original signal. Therefore, also theorthogonal harmonic mode development up to infinity of the frequencyHilbert transform allows, theoretically, to maintain all the informationcontent of the original signal. Each mode contributes to the informationcontent proportionally to the respective power of the mode (assumingthat the overall power of the signal is equal to one). In this respect,FIG. 17 schematically shows the respective power (i.e., informationcontent) associated with each mode up to the eleventh mode. From FIG. 17it can be noted that with the first two or three modes it is possible tomaintain about 90% of the information content of the original signalwith a potential frequency reuse of 1.9. The use of additionalhigher-order modes results in an increase in implementation complexityrather than in an effective improvement in the performances.

Generation of frequency twist, in analogy with time twist generation, isorganized by associating the complex symbol value a_(k)e^(jφ) ^(k) to aset of frequency pulses, properly shifted and phase-rotated.

For the sake of simplicity, it is considered to operate in an OFDMsignal structure, where the main signal is represented by the InverseFast Fourier Transform (IFFT) of the symbol time flow.

In addition to this frequency symbol set, it is added, for each mode, aset of frequency samples.

Modes ±1 are generated repeating the same symbol at 4 differentfrequencies

${\frac{1}{T}\left( {\frac{1}{2} + k} \right)},$

changing each time their phases according to

$^{{\pm j}\; k\frac{\pi}{2}},$

with k=0,1,2,3. This means that the associated IFFT is the sum of 4decimated IFFT, having only 1 row for each sample and each one isweighted by

$0.5\; {^{{\pm j}\; k\frac{\pi}{2}}.}$

Modes ±2 are generated repeating the same symbol at 8 differentfrequencies

${\frac{1}{T}\left( {\frac{3}{4} + k} \right)},$

changing each time their phases according to

$^{{\pm j}\; k\frac{\pi}{4}},$

with k=0,1, . . . , 7. This means that the associated IFFT is the sum of8 decimated IFFT, having only 1 row for each sample and each one isweighted by

$\frac{1}{\sqrt{8}}{^{{\pm j}\; k\frac{\pi}{4}}.}$

In general, modes ±N are generated repeating the same symbol at 2^(N+1)different frequencies

${\frac{1}{T}\left( {\frac{2^{N} - 1}{2^{N}} + k} \right)},$

changing each time their phases according to

$^{{\pm j}\; k\frac{\pi}{2^{N}}},$

with k=0,1, . . . , 2^(N+1)−1. This means that the associated IFFT isthe sum of 4N decimated IFFT, having only 1 row for each sample and eachone is weighted as

$\frac{1}{2^{\frac{N + 1}{2}}}{^{{\pm j}\; k\frac{\pi}{2^{N}}}.}$

In practical terms, phases can be simplified (in terms ofimplementation) assuming the same value each π/2, in this way therotation can be represented by a smaller number of bits.

In this respect, FIGS. 18 and 19 show frequency twist complex functionsfor mode 1 and 2, respectively. From FIGS. 18 and 19 it can be notedthat the bandwidth increases each time that the mode grows. This impliesa sort of increased rigidity of the traditional OFDM structure.

Then, let us take into consideration an OFDM signal architecture, whichcan be considered a sequence of frequency pulses having the shape of asinc. In the same frequency band frequency twisted waves are added andthese additional elements in the following will be called TwistedFrequency frame Units (TFUs). In this respect, FIG. 20 shows an OFDMsuper frame with additional TFUs.

The structure of a TFU is given by the superposition of the OFDMstructure and of the structure of the twisted modes previously defined.

The minimum length of a TFU bandwidth, where modes up to ±/N are used,is given by:

$\frac{2^{N + 1} + 1}{T},$

where T is the time interval duration which is the inverse of thefrequency pulse symbol bandwidth B_(S) (i.e., T=1/B_(S)).

In this respect, FIG. 21 show an approximation of the impulse responseof the frequency Hilbert transform, which approximation uses threemodes.

The mode structure in the TFU frame takes into account the length ofeach mode; therefore, using up to mode ±N, the number M_(MFS) of thefrequency samples of the main mode is:

M _(MFS)=2^(N+1)+1.

It is worth recalling that, assuming B_(S)=1/T, the frequency samples ofgeneric frequency twisted mode ±N are at frequencies

$\frac{1}{T}{\left( {\frac{2^{N} - 1}{2^{N}} + k} \right).}$

Moreover, the number of complex symbol values (or, at reception side, ofcomplex unknowns) of the main mode n=0 is M_(MFS)=2^(N+1)+1, the numberof complex symbol values (or, at reception side, of complex unknowns) ofthe modes +1 and −1 is 2^(N), the number of complex symbol values (or,at reception side, of complex unknowns) of the modes +2 and −2 is2^(N−1), the number of complex symbol values (or, at reception side, ofcomplex unknowns) of the modes +i and −i is 2^(N−i+1), and the number ofcomplex symbol values (or, at reception side, of complex unknowns) ofthe modes +N and −N is 2^(N−N+1)=2.

Therefore, the overall number S_(TOT) of complex symbol values (or ofcomplex unknowns) is given by:

${S_{TOT} = {\left( {2^{N + 1} + 1} \right) + {\sum\limits_{i = 1}^{N}2^{N - i + 1}}}},$

wherein the first addend represents the number M_(MFS) of symbols (or,at reception side, of complex unknowns) of the main mode n=0, while thesecond addend (i.e., the summation) represents the numberS_(TOT)-M_(MFS) of symbols (or, at reception side, of complex unknowns)of all the other modes with n≠0.

The foregoing mathematical formula can be rewritten as:

$S_{TOT} = {{1 + {\sum\limits_{i = 0}^{N}2^{N - i + 1}}} = {1 + {2^{N + 1} \cdot {\sum\limits_{i = 0}^{N}{\left( \frac{1}{2} \right)^{i}.}}}}}$

Thence, since it is known that

${{\sum\limits_{i = 0}^{N}x^{i}} = {{\frac{x^{N + 1} - 1}{x - 1}{\mspace{11mu} \;}{if}\mspace{14mu} x} \neq 1}},$

then it results that:

S _(TOT)=2^(N+2)−1.

The overlapping of frequency pulses associated with different symbolscreates a special form of orthogonality, which depends on the structureof the TFUs. In this sense the TFUs represent a “frequency space” andthe different signals are orthogonal in this space according to symmetryand antisymmetry features of the signal structure. This property can beseen as equivalent to the interferometry in the traditional geometricalspace.

Anyway, even if the present invention deals with “frequency space”, theprocedure for determining the transmitted signals is performed in thetime domain and not in the frequency domain.

In particular, as shown in FIG. 22 which schematically represents theradio communications method according to the present invention (denotedas a whole by 600) as a generalization of the traditional OFDM (orOFDMA) technique (denoted as a whole by 500), the radio communicationsmethod 600 according to the present invention can be considered similarto the traditional OFDM (or OFDMA) technique 500, which, as is broadlyknown, comprises:

at the transmission side, the conversion of a symbol serial time streaminto a parallel independent frequency stream via an Inverse Fast FourierTransform (IFFT) (block 501); and,

at the reception side, the back-transformation into the original symbolserial time stream via a Fast Fourier Transform (FFT) (block 502).

Similarly, the radio communications method 600 according to the presentinvention exploits:

at the transmission side, a “Generalized Inverse Fast Fourier Transform”(GIFFT) (block 601) which includes the implementation of the previouslydescribed frequency Hilbert transform approximation based on frequencytwisted modes; and,

at the reception side, a “Generalized Fast Fourier Transform” (GFFT)(block 602) which includes the extraction of the symbols carried by thefrequency twisted modes.

Let us now consider the structure of the twisted signals in time domainand in frequency domain (on the assumption that for both the domains thefirst mode ±1 is used):

a time twisted mode ±1 signal can be expressed as a)

${{x_{T \pm 1}(t)} = {a_{k}^{{j\phi}_{k}}\left\{ {{\frac{1}{2}\left\lbrack {{{rect}\left( {t - \frac{T}{2}} \right)} - {{rect}\left( {t - \frac{3T}{2}} \right)}} \right\rbrack} \pm {\frac{j}{2}\left\lbrack {{{rect}\left( {t - T} \right)} - {{rect}\left( {t - \frac{5T}{2}} \right)}} \right\rbrack}} \right\}}};$

and

a frequency twisted mode ±1 signal can be expressed as

${X_{F \pm 1}(f)} = {a_{k}^{j\; \phi_{k}}{\left\{ {{\frac{1}{2}\left\lbrack {{{rect}\left( {f - \frac{B}{2}} \right)} - {{rect}\left( {f - \frac{3B}{2}} \right)}} \right\rbrack} \pm {\frac{j}{2}\left\lbrack {{{rect}\left( {f - B} \right)} - {{rect}\left( {f - \frac{5B}{2}} \right)}} \right\rbrack}} \right\}.}}$

The frequency twisted mode ±1 signal is analyzed in time domain therebyresulting that: b)

${x_{F \pm 1}(t)} = {\frac{a_{k}^{{j\phi}_{k}}}{2}\left\{ {\left\lbrack {^{{- {{j2\pi}{({f - \frac{B}{2}})}}}t} - ^{{- {{j2\pi}{({f - \frac{3\; B}{2}})}}}t}} \right\rbrack \pm {j\left\lbrack {^{{- {{j2\pi}{({f - B})}}}t} - ^{{- {{j2\pi}{({f - \frac{5\; B}{2}})}}}t}} \right\rbrack}} \right\}}$$\mspace{20mu} {{{for}\mspace{14mu} {t}} < {\frac{T}{2}.}}$

From a comparison of the signals a) and b) it is evident that thefrequency twist is more robust in keeping the independence of the signalequation system. These feature is evident also from the time behavior ofthe twisted signals, as shown in FIGS. 23 and 24 which illustrate thetime behavior of a time twisted mode +1 signal and of a frequencytwisted mode +1 signal, respectively.

From an ideal point of view the frequency Hilbert transform isapplicable to a time-limited signal. Therefore, in order for thefrequency Hilbert transform to be applicable to a continuous time symbolflow, it is necessary to apply said transform to successive time windowsof said continuous time symbol flow and to identify the beginning andthe end of each time window. This implies that the time window length isincreased of a proper portion so as to render each time windowdetectable. This feature is similar to the bandwidth increase necessaryin the case of time twisted waves.

Therefore, the frequency rotation requires a time interval slightlylarger than the minimum one required by the sampling theorem. Thiscondition is equivalent to consider a symbol duration T_(sym) longerthan the system clock duration T_(cl), as schematically illustrated inFIG. 25.

The above condition implies that, for instance, every 18 frequency bandsan additional one is necessary and that, as a consequence, the bandwidthefficiency is given by 18/19≅0.95. In this respect, FIG. 26 show symboland clock period relationship in the case of 18 signal samples and 19filter samples per frame.

An interesting aspect of this condition applied to the frequency twistedwaves is that it can be interpreted as equivalent to the well-knowncyclic prefix already used with the OFDM technique.

For multiple path transmission the delay spread is generated by the setof different paths between the transmitter and receiver when those pathshave different delays.

As an example, a signal following a direct line-of-sight path wouldarrive before a different version of the same signal which is reflectedby a distant building.

Time domain receivers typically synchronize with each delay spreadcomponent and adjust their individual timings before combining thereceived signals.

When using a rake receiver, each finger belonging to the rake receiversynchronizes itself with a specific delay spread component. The numberof delay spread components which can be combined is, thence, limited tothe number of rake fingers. Any delay spread component which is notcombined appears as interference.

LTE receivers do not need to synchronize themselves with individualdelay spread components, i.e., it is not necessary to adjust the timingof delay spread components, nor it is necessary to do any combining ofdelay spread components. An LTE receiver can operate directly on theaggregate received signal without considering delay spread components.

The cyclic prefix represents a guard period at the start of each OFDMAsymbol which provides protection against multi-path delay spread. Thecyclic prefix also represents an overhead which should be minimized.

The duration of the cyclic prefix should be greater than the duration ofthe multi-path delay spread.

LTE specifies both normal and extended cyclic prefix lengths. The normalcyclic prefix is intended to be sufficient for the majority ofscenarios, while the extended cyclic prefix is intended for scenarioswith particularly high delay spread. Durations for the normal andextended cyclic prefix vary from 7% in the standard case up to 25% inthe extended case. The cyclic prefix is generated by copying the end ofthe main body of the OFDMA symbol at the beginning, as shown in FIG. 27which illustrates the traditional scheme of cyclic prefix forOFDM-OFDMA.

The signal is always continuous at the interface between the cyclicprefix and the main body of the symbol. This results from the main bodyof the symbol always including an integer number of subcarrier cycles.

FIG. 28 shows an example of 2 delay spread components. The second delayspread component is received later than the first delay spreadcomponent. An FFT processing window is defined at the receiver:

the processing window captures the main body of the OFDMA symbolbelonging to the first delay spread component; the cyclic prefixbelonging to the first delay spread component is discarded;

the processing window captures part of the cyclic prefix and themajority of the main body of the OFDMA symbol belonging to the seconddelay spread component; sections of the cyclic prefix and main body ofthe OFDMA symbol which fall outside the processing window are discarded;and,

in the extreme case, where the delay spread is equal to the duration ofthe cyclic prefix, the FFT processing window fully captures the cyclicprefix belonging to the delay spread component and discards a section ofthe main body of the ODFMA symbol which has a duration equal to thecyclic prefix.

The time domain representation of each delay spread component within theprocessing window is different, however, the frequency domainrepresentation of each delay spread component within the processingwindow is identical.

Let us now come back to the description of the present invention and letus assume that modes up to N=±2 are used, then the band occupied by theTFU configuration is given by (2 ²⁺¹+1)=9 frequency slots. To this TFUcorresponds a Twisted Time frame Unit (TTU), which is increased to avoidtime duration ambiguities. If one half slot is considered, the TTUincreases of 1/(2B_(sym)) and the total length of the TTU is9.5/B_(sym). In this respect, FIG. 29 shows time frame duration increasedue to cyclic prefix (CP).

This increase is much lower than the one required by OFDMA. This impliesthat in practical system there is no additional loss for includingfrequency twisted waves in the OFDM (or OFDMA) super frame.

The increase of time interval duration creates automatically a replicaof the signal at the beginning of the time interval itself, without anychange in the occupied frequency bandwidth.

This approach is, thence, much more interesting for the understanding ofthe physical meaning of the cyclic prefix, than the ordinary explanationabout its use.

Considering sampling in frequency domain at a symbol rate slightlysmaller than the clock rate, the signal in time domain, on theassumption that only the main mode is used, has the time behavior shownin FIG. 30, where the sinusoid are not exactly a multiple of the symbolperiod: i.e., what the cyclic prefix is performing.

Adding the FTUs, the twisted mode signals present the same behavior ofthe main mode signal, as shown in FIG. 31.

Increasing the number of TTUs, the number of sinusoidal signalincreases, but the ratio between T_(cl) and T_(sym) remains unchanged.

The OFDM-twisted frequency has two hierarchical levels:

the former is related to the TTUs structure; and

the latter is related to the assembly of the TFUs constituting the OFDMstructure.

Both the levels have the same time duration and the difference is givenby the component frequency blocks:

each TFU corresponds to a number of samples defined by the twistedfrequency structure, which introduces additional frequency sampleslocated between the main frequency samples;

the super frame structure is a set of TTUs, centered at the properfrequency, and a set of traditional OFDM frequency samples, if wished;

the standard frequency samples can simplify the process ofsynchronization and phasing.

In order to consider the impact of thermal noise on the twisted waves,it is important to consider what happens on the time twisted waves,because there is a very interesting difference between the two familiesof twisted waves, which can have important applications intelecommunications, especially in the case of mobile LTE ones.

The noise level for the time twisted waves can be represented as dividedinto two parts:

a first part related to the symbol rate bandwidth; and

a second part related to the difference between the symbol rate and theclock bandwidth.

In this respect, FIG. 32 schematically illustrates noise bandwidths fortime twisted waves: one defined according to minimum Nyquist bandwidth,the other related to the bandwidth increase for solving ambiguityaspects.

The above noise structure can be written as:

${{{n_{t}(t)}^{{j2\pi}\; f_{0}t}} = {{{n_{{int}\; B}(t)}^{{j2\pi}\; f_{0}t}} + {\frac{1}{\sqrt{2}}{{n_{ext}(t)}\left\lbrack {^{{{j2\pi}{({f_{0} + \frac{B + {\Delta \; {B/2}}}{2}})}}t} + ^{{{j2\pi}{({f_{0} - \frac{B + {\Delta \; {B/2}}}{2}})}}t}} \right\rbrack}}}},$

where n_(intB)(t) denotes the noise part related to the symbol ratebandwidth, and n_(ext)(t)=n_(extΔB)(t)e^(jφ) ^(ΔB) ^((t)) denotes theadditional noise part due to the need of avoiding ambiguities on thesymbol rate phasing.

n_(intB)(t), when sampled at the symbol rate, is an even function (noinformation on the odd sampling).

Moreover,

$\sqrt{2}{n_{{ext}\; \Delta \; B}(t)}^{{j2\pi}\; f_{0}t}{\cos \left\lbrack {{2{\pi \left( \frac{B + {\Delta \; {B/2}}}{2} \right)}t} + {\phi_{\Delta \; B}(t)}} \right\rbrack}$

causes an additional contribution on the even and odd components.

With reference to FIG. 32, the noise in the Nyquist band can berepresented by a sinc time pulse, which is an even function, while thetwo sidebands can be represented by an even and an odd component.

In terms of relationship between the noise components, it can bewritten:

${\frac{{noise}_{even}}{{noise}_{odd}} \cong \frac{B + {\Delta \; B}}{\Delta \; B}} = {1 + {\frac{B}{\Delta \; B}.}}$

Considering the above for a simplified rect filter, the odd modes can bepresented as:

${{{POWER}\mspace{14mu} {MODES}_{N}} = {2{\sum\limits_{k = 1}^{N}\left( \frac{2}{k\; \pi} \right)^{2}}}},$

for the first modes ±1 there results

${\frac{8}{\pi^{2}} \cong 0.81};$

${\left( \frac{C}{N} \right)_{odd} = {\frac{0.81\Delta \; B}{B + {\Delta \; B}}\sigma_{t}}},$

for a bandwidth increase of 1 over 18 there results

${\left( \frac{C}{N} \right)_{odd} = {{{- 11.8} + {\sigma_{tdB}{dB}}} = {{- 11.8} + {\left( \frac{C}{N} \right)_{even}{dB}}}}};$

the 11.8 dB term can be considered as the minimum gain against unwishedinterferences.

Instead, as far as the case of frequency twisted waves is concerned, thenoise spectrum occupies the bandwidth W and there is not any possibilityof separating, in the time domain, its even and odd components for asingle frequency pulse, as shown in FIG. 33 (which schematicallyillustrates noise impact in the case of frequency twisted waves).

In fact, in the time domain the noise signal samples are not associatedwith the main signal samples, but they are distributed all along thetime interval, which is utilized for reconstructing the frequencysampling value (FET). Therefore it is not possible to associate the maincontribution of the noise to the main samples and there is no additionaladvantage for higher modes, as in the case of time rotation.

The twisted waves add independent communication channels, one for eachmode, and the information capacity increases with respect to the one ofthe single channel associated with the main mode.

The above is valid for both frequency twist and time twist, but it isvery interesting to analyze the similarities and the differences inorder to optimize the use of the two twisting processes according to theoverall system conditions.

In general terms, it is possible to perform a system comparison on thebasis of what presented in the foregoing and in PCT/FR2013/052636. Inparticular, the following TABLE I presents a comparison between timetwisted waves and frequency twisted waves at system level, whereinsupplementary references are provided for single carrier case and OFDMcase.

TABLE I Parameter assuming as reference Time Frequency OFDMS/N_(thermal) = Twist Twist Single (parameters 13.9 dB QPSK (2 modes) (2modes) carrier from LTE) Linearity 1.5 4.5 1.5 4.5 (HPA outputback-off - dB) S/N with 10 12.7 10.5  12.7 interference (dB) Bandwidth33% 0% 12.5%   0% increase (with respect to 1/T_(S), including roll-off)Time increase  0% 5%   0% 7-25% (with respect to 1/B_(S))Self-interference −28 −28 −35     −35 (dB) Additional 0.5 0 0   0thermal noise BER for main 6*10⁻³ 1.2*10⁻⁴ 3*10⁻³ 1.2*10⁻⁴ mode (nocode) BER for higher 8*10⁻⁴ 1.2*10⁻⁴ NA NA modes (no code) Spectralefficiency 2.5 3.1-2.5 1.8 1.9-1.5 (bit/s/Hz) Shannon limit 3.5 5.4 3.65.4 (one channel - bit/s/Hz) Shannon limit 5.5 6.9 5.8 6.9 for twist

In summary, time twist operates better in those cases in which theamplifiers work closer to the saturation, while frequency twist operatesbetter when linearity can be preserved. That is a general condition forstandard transmission too. In fact, it is well known that, in the caseof LTE, on the Forward link (i.e., from the Base Station to mobiledevice) OFDM is used, while on the Return link (i.e., from the mobiledevice to the Base Station) Single Channel FDMA is preferred.

FIG. 34 schematically shows (link) spectral efficiency (bit/s/Hz) as afunction of the energy per symbol over noise density (E_(symbol)/N₀) forfrequency twisted waves, on the assumption that there are presentthermal noise and self-interference, which is the noise due to theinterference between side-by-side frames.

In particular, FIG. 34 shows that the behavior (in terms of bit/s/Hz) offrequency twisted wave modes presents values that are always lower thanthe main mode, due to the absence of the noise reduction for twistedmodes.

In the time domain the noise signal samples are not associated with themain signal samples, which are essentially complex values of frequencysamples. They are distributed all along the time interval, which isutilized for reconstructing the frequency sampling value (FFT).Therefore, it is not possible to associate the main contribution of thenoise with the main samples and there is no additional advantage forhigher modes, as in the case of time rotation.

As far as the transmitter according to the present invention isconcerned, the generation of transmission signals is based on thetransformation of a symbol serial time flow frames into a parallel flowfor each frame, which is equivalent to the generation of a number ofsinusoidal signal in the time window frame.

This process is known and used for OFDM (or OFDMA) architecture; it isequivalent to an IFFT operation. In the case of OFDM, the frequencysamples are spaced according to the sampling theorem applied to thefrequency domain.

When using frequency twisted waves, it is necessary to oversampling theoverall frequency band via the introduction of additional frequencysamples, spaced as previously defined for each mode.

In this respect, it is worth recalling that generic modes ±N aregenerated repeating the same symbol at 2^(N+1) different frequencies

${\frac{1}{T}\left( {\frac{2^{N} - 1}{2^{N}} + k} \right)},$

changing each time their phases according to

$^{{\pm j}\; k\frac{\pi}{2^{N}}},$

with k=0,1, . . . , 2^(N+1)−1. This means that the associated IFFT isthe sum of 4N decimated IFFT, having only 1 row for each sample and eachone is weighted as

$\frac{1}{2^{\frac{N + 1}{2}}}{^{{\pm j}\; k\; \frac{\pi}{2^{N}}}.}$

A preferred use of frequency twisted waves is inside an OFDM-OFDMAarchitecture. Taking into consideration that an OFDM structure includesa very large number of frequencies, a possible architecture is proposedhere below.

On the assumption that modes up to N=±2 are used, the band occupied bythis configuration is given by 2²⁺¹+1=9 frequency slots. This section iscalled Twisted Frequency frame Unit (TFU) and to this TFU corresponds aTwisted Time frame Unit (TTU).

The inclusion of the TFU cyclic prefix increases the time frame by

$\frac{0.5}{B_{S}}$

and, thence, for the TTU there results

$\frac{9.5}{B_{S}}.$

The cyclic prefix is used for each TFU present in the full OFDM-OFDMAbandwidth (and, as previously explained, is physically the same one usedfor OFDM, but used for each TFU).

As previously explained, the OFDM-twisted frequency has two hierarchicallevels:

the former is related to the TTUs structure, which depends on the numberof modes chosen and the number of frequency slots adopted; and

the latter is related to the assembly of the TFUs constituting the OFDMstructure.

Again as previously explained, both the levels have the same timeduration and the difference is given by the component frequency blocks:

each TFU corresponds to a number of samples defined by the twistedfrequency structure, which introduces additional frequency sampleslocated between the main frequency samples;

the super frame structure is a set of TTUs, centered at the properfrequency, and a set of traditional OFDM frequency samples, if wished;

the standard frequency samples can simplify the process ofsynchronization and phasing.

The generation of the main mode signal and of the twisted mode signalsvia this process is called, as previously explained, Generalized InverseFast Fourier Transform (GIFFT).

For the sake of simplicity, it is assumed to use twisted modes ±1 and±2. This implies, as previously explained, the presence of 9 frequencyslots related to the main mode; the frequency rotation requires a timeinterval slightly larger than the minimum one required by the samplingtheorem in order to avoid ambiguities, due to the determination of theframe boundary; this implies that, for instance, every 18 frequency bandone additional one is necessary; therefore, there are two time referencewindow: one defined by the clock T_(cl), and one defined by the symbolT_(sym). The relationship between T_(cl) and T_(sym) is given by:

${T_{sym} = {\frac{2^{k + 2} + 3}{2^{k + 2} + 2}T_{cl}}},{where}$$\frac{1}{2^{k + 2} + 2}T_{cl}$

is equivalent to the cyclic prefix.

In the present case,

T _(sym)=19/18T_(cl), and

-   -   1/18T_(cl) is the cyclic prefix.

In order to create the correct reference between the real and theimaginary signals, it is important to avoid possible ambiguities on thezero of the reference system. In fact, this system shall be used as thereference system of the principal value of the Cauchy integral.

Therefore, it is important to have a sampling rate slightly larger thanthe minimum possible for the symbol rate associated with the plane wavemode.

The frequency representation is shown in FIG. 35, which schematicallyillustrates frequency slots with the additional one for ambiguityresolution (always on the assumption that twisted modes up to ±2 areused). This additional frequency slot implies that the bandwidth of eachsymbol is smaller than the maximum one given by Nyquist criterion, andthat the additional time duration creates the repetition of part of thesinusoidal at the beginning of the time slot (as in the case of“traditional” cyclic prefix).

The main mode has the same structure of the traditional IFFT, but thesampling is performed 19 times instead of 18.

Higher-order modes are generated considering that each of them can bederived considering a set of frequency pulses properly shifted infrequency and phased (either 1;±j;−1; +j).

The frequency pulses of each mode are properly positioned via atransformation algorithm, which is very similar to the IFFT, having inmind the fact that the starting frequency is properly positioned on thefrequency axis and that more samples are associated with the samesymbol, as explained in the foregoing.

In order for the operation of the present invention to be betterunderstood, reference is made to FIG. 36, which shows a functional blockdiagram of a transmitting system (denoted as whole by 7) according to anillustrative embodiment of the present invention.

In particular, the transmitting system 7 shown in FIG. 36 is designed togenerate frequency twisted waves up to modes ±3, and comprises:

a symbol generation section 70 configured to generate and output adigital symbol stream;

a frequency twisted mode generation unit 700 based on GIFFT, saidfrequency twisted mode generation unit 700 being coupled with the symbolgeneration section 70 to receive the digital symbol stream outputted bythe latter, and being configured to generate and output, for eachsequence of S_(TOT) digital symbols received from the symbol generationsection 70 (in particular, in the example shown in FIG. 36, S_(TOT)=31),a respective digital time signal obtained by transforming from frequencydomain to time domain

-   -   main mode frequency samples carrying M_(MFS) of said S_(TOT)        received digital symbols (in particular, in the example shown in        FIG. 36, M_(MFS)=17) via a frequency main mode (preferably, as        previously explained, the main mode frequency samples are        OFDM/OFDMA-type frequency samples), and    -   twisted mode frequency samples carrying the other        S_(TOT)-M_(MFS) received digital symbols via frequency twisted        modes, wherein, in the example shown in FIG. 36, the twisted        mode frequency samples include    -   frequency samples which are related to frequency twisted mode +1        and which carry four respective digital symbols via the        frequency twisted mode +1,    -   frequency samples which are related to frequency twisted mode −1        and which carry four respective digital symbols via the        frequency twisted mode −1,    -   frequency twisted mode which are related to frequency twisted        mode +2 and which carry two respective digital symbols via the        frequency twisted mode +2,    -   frequency twisted mode which are related to frequency twisted        mode −2 and which carry two respective digital symbols via the        frequency twisted mode −2,    -   frequency twisted mode which are related to frequency twisted        mode +3 and which carry one respective digital symbol via the        frequency twisted mode +3, and    -   frequency twisted mode which are related to frequency twisted        mode −3 and which carry one respective digital symbol via the        frequency twisted mode −3; and

an RF transmission section 7000 which is coupled with the frequencytwisted mode generation unit 700 to receive the digital time signalsoutputted by the latter, and which is configured to transmit atpredefined radio frequencies the received digital time signals by meansof a single antenna or a plurality of antennas/antenna elements (notshown in FIG. 36 for the sake of illustration simplicity).

Conveniently, the aforesaid predefined radio frequencies can range froma few KHz to hundreds of GHz depending on the specific application forwhich the transmitting system 7 is designed.

Preferably, the transmitting system 7 is a device/system for wirelesscommunications based on OFDM and/or OFDMA, or, more preferably, on LTEand/or WiMAX.

Conveniently, the symbol generation section 70 is designed to generatethe digital symbol stream by performing several operations, such as thefollowing operations (not necessarily all performed and not necessarilyperformed in the following sequence): information encoding (convenientlyby performing one or more signal modulations), one or more frequencyshifting operations, one or more analog-to-digital conversionoperations, and one or more filtering operations.

Again conveniently, the RF transmission section 7000 can be designed totransmit at the predefined radio frequencies the digital time signals byperforming several operations, such as the following operations (notnecessarily all performed and not necessarily performed in the followingsequence): frequency up-shifting (in particular. from IntermediateFrequency (IF) up to RF), one or more filtering operations, one or moredigital-to-analog conversion operations, and power amplification.

More in detail, as shown in FIG. 36, the frequency twisted modegeneration unit 700 includes:

a frequency main mode generation module 701, which, in use,

-   -   determines, for each of said M_(MFS)=17 digital symbols, a        corresponding symbol complex value a_(p)e^(jφ) ^(p) (with p=1,2,        . . . , M_(MFS)) which represents said digital symbol,    -   allocates each of the M_(MFS) symbol complex values to a        respective frequency p/T, or (since T=1/B_(S)) p·B_(S) (as in        the case of traditional OFDM/OFDMA technique), thereby obtaining        M_(MFS) main mode frequency samples, and    -   performs an IFFT of all the M_(MFS) main mode frequency samples,        thereby generating a digital time signal related to the        frequency main mode;

a frequency twisted mode +1 generation module 702, which, in use,

-   -   determines, for the first of the four respective digital        symbols, a corresponding symbol complex value a_(+1;1)e^(jφ)        ^(+1;1) which represents said digital symbol,    -   allocates said symbol complex value a_(+1;1)e^(jφ) ^(+1;1) to        four respective frequencies B_(S)(1/2+k) (with k=0,1,2,3)        changing, for each frequency sample, the respective phase        according to

$^{{+ j}\; k\; \frac{\pi}{2}}$

and weighting each frequency sample by 1/2 (i.e., multiplying, for eachof the four respective frequencies, the symbol complex valuea_(+1;1)e^(jφ) ^(+1;1) by a respective complex coefficient

$\left. \frac{^{{+ j}\; k\frac{\pi}{2}}}{2} \right),$

thereby obtaining four twisted mode frequency samples which are relatedto the frequency twisted mode +1 and which carry said first respectivedigital symbol via said frequency twisted mode +1,

-   -   determines, for the second of the four respective digital        symbols, a corresponding symbol complex value a_(+1;2)e^(jφ)        ^(+1;2) which represents said digital symbol,    -   allocates said symbol complex value a_(+1;2)e^(jφ) ^(+1;2) to        four respective frequencies B_(S)(1/2+k) (with k=4,5,6,7)        changing, for each frequency sample, the respective phase        according to

$^{{+ {j{({k - 4})}}}\frac{\pi}{2}}$

and weighting each frequency sample by 1/2 (i.e., multiplying, for eachof the four respective frequencies, the symbol complex valuea_(+1;2)e^(jφ) ^(+1;2) by a respective complex coefficient

$\left. \frac{^{{+ {j{({k - 4})}}}\frac{\pi}{2}}}{2} \right),$

thereby obtaining four further twisted mode frequency samples which arerelated to the frequency twisted mode +1 and which carry said secondrespective digital symbol via said frequency twisted mode +1,

-   -   determines, for the third of the four respective digital        symbols, a corresponding symbol complex value a_(+1;3)e^(jφ)        ^(+1;3) which represents said digital symbol,    -   allocates said symbol complex value a_(+1;3)e^(jφ) ^(+1;3) to        four respective frequencies B_(S)(1/2+k) (with k=8,9,10,11)        changing, for each frequency sample, the respective phase        according to

$^{{+ {j{({k - 8})}}}\frac{\pi}{2}}$

and weighting each frequency sample by 1/2 (i.e., multiplying, for eachof the four respective frequencies, the symbol complex valuea_(+1;3)e^(jφ) ^(+1;3) by a respective complex coefficient

$\left. \frac{^{{+ {j{({k - 8})}}}\frac{\pi}{2}}}{2} \right),$

thereby obtaining four further twisted mode frequency samples which arerelated to the frequency twisted mode +1 and which carry said thirdrespective digital symbol via said frequency twisted mode +1,

-   -   determines, for the fourth of the four respective digital        symbols, a corresponding symbol complex value a_(+1;4)e^(jφ)        ^(+1;4) which represents said digital symbol,    -   allocates said symbol complex value a_(+1;4)e^(jφ) ^(+1;4) to        four respective frequencies B_(S)(1/2+k) (with k=12,13,14,15)        changing, for each frequency sample, the respective phase        according to

$^{{+ {j{({k - 12})}}}\frac{\pi}{2}}$

and weighting each frequency sample by 1/2 (i.e., multiplying, for eachof the four respective frequencies, the symbol complex valuea_(+1;4)e^(jφ) ^(+1;4) by a respective complex coefficient

$\left. \frac{^{{+ {j{({k - 12})}}}\frac{\pi}{2}}}{2} \right),$

thereby obtaining four final twisted mode frequency samples which arerelated to the frequency twisted mode +1 and which carry said fourthrespective digital symbol via said frequency twisted mode +1, and

-   -   performs an IFFT of all the sixteen twisted mode frequency        samples related to the frequency twisted mode +1, thereby        generating a digital time signal related to the frequency        twisted mode +1;

a frequency twisted mode −1 generation module 703, which, in use,

-   -   determines, for the first of the four respective digital        symbols, a corresponding symbol complex value a_(−1;1)e^(jφ)        ^(−1;1) which represents said digital symbol,    -   allocates said symbol complex value a_(−1;1)e^(jφ) ^(−1;1) to        four respective frequencies B_(S)(1/2+k) (with k=0,1,2,3)        changing, for each frequency sample, the respective phase        according to

$^{{- j}\; k\frac{\pi}{2}}$

and weighting each frequency sample by 1/2 (i.e., multiplying, for eachof the four respective frequencies, the symbol complex valuea_(−1;1)e^(jφ) ^(−1;1) by a respective complex coefficient

$\left. \frac{^{{- j}\; k\frac{\pi}{2}}}{2} \right),$

thereby obtaining four twisted mode frequency samples which are relatedto the frequency twisted mode −1 and which carry said first respectivedigital symbol via said frequency twisted mode −1,

-   -   determines, for the second of the four respective digital        symbols, a corresponding symbol complex value a_(−1;2)e^(jφ)        ^(−1;2) which represents said digital symbol,    -   allocates said symbol complex value a_(−1;2)e^(jφ) ^(−1;2) to        four respective frequencies B_(S)(1/2+k) (with k=4,5,6,7)        changing, for each frequency sample, the respective phase        according to

$^{{- {j{({k - 4})}}}\; \frac{\pi}{2}}$

and weighting each frequency sample by 1/2 (i.e., multiplying, for eachof the four respective frequencies, the symbol complex valuea_(−1;2)e^(jφ) ^(−1;2) by a respective complex coefficient

$\left. \frac{^{{- {j{({k - 4})}}}\frac{\pi}{2}}}{2} \right),$

thereby obtaining four further twisted mode frequency samples which arerelated to the frequency twisted mode −1 and which carry said secondrespective digital symbol via said frequency twisted mode −1,

-   -   determines, for the third of the four respective digital        symbols, a corresponding symbol complex value a_(−1;3)e^(jφ)        ^(−1;3) which represents said digital symbol,    -   allocates said symbol complex value a_(−1;3)e^(jφ) ^(−1;3) to        four respective frequencies B_(S)(1/2+k) (with k=8,9,10,11)        changing, for each frequency sample, the respective phase        according to

$^{{- {j{({k - 8})}}}\frac{\pi}{2}}$

and weighting each frequency sample by 1/2 (i.e., multiplying, for eachof the four respective frequencies, the symbol complex valuea_(−1;3)e^(jφ) ^(−1;3) by a respective complex coefficient

$\left. \frac{^{{- {j{({k - 8})}}}\; \frac{\pi}{2}}}{2} \right),$

thereby obtaining four further twisted mode frequency samples which arerelated to the frequency twisted mode −1 and which carry said thirdrespective digital symbol via said frequency twisted mode −1,

-   -   determines, for the fourth of the four respective digital        symbols, a corresponding symbol complex value a_(−1;4)e^(jφ)        ^(−1;4) which represents said digital symbol,    -   allocates said symbol complex value a_(−1;4)e^(jφ) ^(−1;4) to        four respective frequencies B_(S)(1/2+k) (with k=12,13,14,15)        changing, for each frequency sample, the respective phase        according to

$^{{- {j{({k - 12})}}}\frac{\pi}{2}}$

and weighting each frequency sample by 1/2 (i.e., multiplying, for eachof the four respective frequencies, the symbol complex valuea_(−1;4)e^(jφ) ^(−1;4) by a respective complex coefficient

$\left. \frac{^{{- j}\; {({k - 12})}\frac{}{2}}}{2} \right),$

thereby obtaining four final twisted mode frequency samples which arerelated to the frequency twisted mode −1 and which carry said fourthrespective digital symbol via said frequency twisted mode −1, and

-   -   performs an IFFT of all the sixteen twisted mode frequency        samples related to the frequency twisted mode −1, thereby        generating a digital time signal related to the frequency        twisted mode +1;

a frequency twisted mode +2 generation module 704, which, in use,

-   -   determines, for the first of the two respective digital symbols,        a corresponding symbol complex value a_(+2;1)e^(jφ) ^(+2;1)        which represents said digital symbol,    -   allocates said symbol complex value a_(+2;1)e^(jφ) ^(+2;1) to        eight respective frequencies B_(S)(3/4+k) (with k=0,1, . . .        , 7) changing, for each frequency sample, the respective phase        according to

$^{{+ j}\; k\frac{}{4}}$

and weighting each frequency sample by 1/√{square root over (8)} (i.e.,multiplying, for each of the eight respective frequencies, the symbolcomplex value a_(+2;1)e^(jφ) ^(+2;1) by a respective complex coefficient

$\left. \frac{^{{+ j}\; k\frac{}{4}}}{\sqrt{8}} \right),$

thereby obtaining eight twisted mode frequency samples which are relatedto the frequency twisted mode +2 and which carry said first respectivedigital symbol via said frequency twisted mode +2,

-   -   determines, for the second of the two respective digital        symbols, a corresponding symbol complex value a_(+2;2)e^(jφ)        ^(+2;2) which represents said digital symbol,    -   allocates said symbol complex value a_(+2;2)e^(jφ) ^(+2;2) to        eight respective frequencies B_(S)(3/4+k) (with k=8,9, . . .        , 15) changing, for each frequency sample, the respective phase        according to

$^{{+ {j{({k - 8})}}}\frac{\pi}{4}}$

and weighting each frequency sample by 1/√{square root over (8)} (i.e.,multiplying, for each of the eight respective frequencies, the symbolcomplex value a_(+2;2)e^(jφ) ^(+2;2) by a respective complex coefficient

$\left. \frac{^{{+ {j{({k - 8})}}}\frac{}{4}}}{\sqrt{8}} \right),$

thereby obtaining eight further twisted mode frequency samples which arerelated to the frequency twisted mode +2 and which carry said secondrespective digital symbol via said frequency twisted mode +2, and

-   -   performs an IFFT of all the sixteen twisted mode frequency        samples related to the frequency twisted mode +2, thereby        generating a digital time signal related to the frequency        twisted mode +2;

a frequency twisted mode −2 generation module 705, which, in use,

-   -   determines, for the first of the two respective digital symbols,        a corresponding symbol complex value a_(−2;1)e^(jφ) ^(−2;1)        which represents said digital symbol,    -   allocates said symbol complex value a_(−2;1)e^(jφ) ^(−2;1) to        eight respective frequencies B_(S)3/4+k) (with k=0,1, . . . , 7)        changing, for each frequency sample, the respective phase        according to

$^{{- j}\; k\frac{\pi}{4}}$

and weighting each frequency sample by 1/√{square root over (8)} (i.e.,multiplying, for each of the eight respective frequencies, the symbolcomplex value a_(−2;1)e^(jφ) ^(−2;1) by a respective complex coefficient

$\left. \frac{^{{- j}\; k\frac{\pi}{4}}}{\sqrt{8}} \right),$

thereby obtaining eight twisted mode frequency samples which are relatedto the frequency twisted mode −2 and which carry said first respectivedigital symbol via said frequency twisted mode −2,

-   -   determines, for the second of the two respective digital        symbols, a corresponding symbol complex value a_(−2;2)e^(jφ)        ^(−2;2) which represents said digital symbol,    -   allocates said symbol complex value a_(−2;2)e^(jφ) ^(−2;2) to        eight respective frequencies B_(S)(3/4+k) (with k=8,9, . . .        , 15) changing, for each frequency sample, the respective phase        according to

$^{{- {j{({k - 8})}}}\frac{\pi}{4}}$

and weighting each frequency sample by 1/√{square root over (8)} (i.e.,multiplying, for each of the eight respective frequencies, the symbolcomplex value a_(−2;2)e^(jφ) ^(−2;2) by a respective complex coefficient

$\left. \frac{^{{- {j{({k - 8})}}}\frac{\pi}{4}}}{\sqrt{8}} \right),$

thereby obtaining eight further twisted mode frequency samples which arerelated to the frequency twisted mode −2 and which carry said secondrespective digital symbol via said frequency twisted mode −2, and

-   -   performs an IFFT of all the sixteen twisted mode frequency        samples related to the frequency twisted mode −2, thereby        generating a digital time signal related to the frequency        twisted mode −2;

a frequency twisted mode +3 generation module 706, which, in use,

-   -   determines, for the respective digital symbol, a corresponding        symbol complex value a₊₃e^(jφ) ⁺³ which represents said digital        symbol,    -   allocates said symbol complex value a₊₃e^(jφ) ⁻³ to sixteen        respective frequencies B_(S)(7/8+k) (with k=0,1, . . . , 15)        changing, for each frequency sample, the respective phase        according to

$^{{+ j}\; k\frac{\pi}{8}}$

and weighting each frequency sample by 1/4 (i.e., multiplying, for eachof the sixteen respective frequencies, the symbol complex valuea₊₃e^(jφ) ⁺³ by a respective complex coefficient

$\left. \frac{^{{+ j}\; k\frac{\pi}{8}}}{4} \right),$

thereby obtaining sixteen twisted mode frequency samples which arerelated to the frequency twisted mode +3 and which carry said respectivedigital symbol via said frequency twisted mode +3, and

-   -   performs an IFFT of all the sixteen twisted mode frequency        samples related to the frequency twisted mode +3, thereby        generating a digital time signal related to the frequency        twisted mode +3;

a frequency twisted mode −3 generation module 707, which, in use,

-   -   determines, for the respective digital symbol, a corresponding        symbol complex value a⁻³e^(jφ) ⁻³ which represents said digital        symbol,    -   allocates said symbol complex value a⁻³e^(jφ) ⁻³ to sixteen        respective frequencies B_(S)(7/8+k) (with k=0,1, . . . , 15)        changing, for each frequency sample, the respective phase        according to

$^{{- j}\; k\frac{\pi}{8}}$

and weighting each frequency sample by 1/4 (i.e., multiplying, for eachof the sixteen respective frequencies, the symbol complex valuea⁻³e^(jφ) ⁻² by a respective complex coefficient

$\left. \frac{^{{- j}\; k\frac{\pi}{8}}}{4} \right),$

thereby obtaining sixteen twisted mode frequency samples which arerelated to the frequency twisted mode −3 and which carry said respectivedigital symbol via said frequency twisted mode −3, and

-   -   performs an IFFT of all the sixteen twisted mode frequency        samples related to the frequency twisted mode −3, thereby        generating a digital time signal related to the frequency        twisted mode −3; and

a combining module 708, which, in use, combines (namely, adds together)the digital time signals outputted by the frequency main mode generationmodule 701 (i.e., the digital time signal related to the frequency mainmode), by the frequency twisted mode +1 generation module 702 (i.e., thedigital time signal related to the frequency twisted mode +1), by thefrequency twisted mode −1 generation module 703 (i.e., the digital timesignal related to the frequency twisted mode −1), by the frequencytwisted mode +2 generation module 704 (i.e., the digital time signalrelated to the frequency twisted mode +2), by the frequency twisted mode−2 generation module 705 (i.e., the digital time signal related to thefrequency twisted mode −2), by the frequency twisted mode +3 generationmodule 706 (i.e., the digital time signal related to the frequencytwisted mode +3), and by the frequency twisted mode −3 generation module707 (i.e., the digital time signal related to the frequency twisted mode−3), thereby generating an overall digital time signal.

Linearity of the frequency twisted mode generation unit 700 isimportant, due to the presence of a wide multicarrier architecture.

Conveniently, the frequency twisted mode generation unit 700 carries outall the aforesaid operations of by using an overall complex transmissionmatrix [[GIFFT]] designed to implement, in a combined way and at one andthe same time, all the aforesaid operations so that, when applied to asequence of S_(TOT) digital symbols received from the symbol generationsection 70, time samples of the corresponding digital time signal areautomatically computed by the frequency twisted mode generation unit700.

Preferably, for each digital time signal generated and outputted by thecombining module 708, the frequency twisted mode generation unit 700 isfurther designed to insert, at the beginning of said digital timesignal, a respective cyclic prefix which is a replica of an end portionof said digital time signal (in accordance with what was previouslyexplained).

Let us now consider the operation of the present invention at receptionside, and, in this respect, reference is made to FIG. 37, which shows afunctional block diagram of a receiving system (denoted as whole by 8)according an illustrative embodiment of the present invention.

In particular, as shown in FIG. 37, the receiving system 8 comprises:

an RF reception section 8000, which is designed to receive the RFsignals transmitted at the predefined radio frequencies by thetransmitting system 7 (in particular, by the RF transmission section7000); said RF reception section 8000 being designed to receive the RFsignals by means of a single antenna or a plurality of antennas/antennaelements (not shown in FIG. 37 for the sake of illustration simplicity),and to process the received RF signals so as to obtain, on the basis ofsaid received RF signals, an incoming digital signal;

a symbol extraction unit 800 based on GFFT, which is coupled with saidRF reception section 8000 to receive the incoming digital signaltherefrom, and which is designed to

-   -   process said incoming digital signal so as to extract the        digital symbols carried by said incoming digital signal, and    -   output a stream of extracted digital symbols; and

a symbol processing section 80, which is coupled with said symbolextraction unit 800 to receive the stream of extracted digital symbolsoutputted by the latter, and which is designed to process said stream ofextracted digital symbols.

The aforesaid predefined radio frequencies coincide with the radiofrequencies used in transmission by the transmitting system 7, inparticular by the RF transmission section 7000. Conveniently, as alreadysaid, the predefined radio frequencies can range from a few KHz tohundreds of GHz depending on the specific application which the overallradio communications system comprising the transmitting system 7 and thereceiving system 8 is designed for.

Preferably, the receiving system 8 is a device/system for wirelesscommunications based on OFDM and/or OFDMA, or, more preferably, on LTEand/or WiMAX.

Conveniently, the RF reception section 8000 is designed to obtain theincoming digital signal by performing several operations upon thereceived RF signals, such as the following operations (not necessarilyall performed and not necessarily performed in the following sequence):low-noise amplification, one or more frequency down-shifting operations(in particular from RF down to IF), one or more filtering operations,and one or more analog-to-digital conversion operations.

Again conveniently, the symbol processing section 80 is designed toprocess the stream of extracted digital symbols by performing severaloperations, such as the following operations (not necessarily allperformed and not necessarily performed in the following sequence): oneor more filtering operations, one or more digital-to-analog conversionoperations, one or more frequency shifting operations, and informationdecoding (conveniently by performing one or more signal demodulations).

At the reception side the parallel signal flow is to be considered, asin the case of OFDM (or OFDMA), and a reception matrix [[GFFT]] is usedby the symbol extraction unit 800 to extract the digital symbols carriedby the incoming digital signal.

The main difference with respect to the standard OFDM signal is thatOFDM exploits Hermitian matrices, while in the case of frequency twistedwaves the transmission matrix [[GIFFT]] is rectangular and, thence, inorder for the reception matrix [[GFFT]] to be obtained, pseudo-inverseapproach is exploited. The use of such a procedure is called GeneralizedFast Fourier Transform (GFFT) and is somewhat similar to the GeneralizedMatched Filter used for the time twisted waves and described inPCT/FR2013/052636.

In use, the symbol extraction unit 800 processes the incoming digitalsignal by using a time window T_(Sym) (including the cyclic prefix) soas to process successive, non-overlapped portions of the incomingdigital signal each having a time duration equal to T_(Sym), and toextract the digital symbols respectively carried by each incomingdigital signal portion.

The input sequence in the time window T_(Sym) is oversampled with thesame law of the transmission flow; on the assumption that modes up to ±Nare used, the size of the reception matrix is given by:

the number of unknowns (i.e., symbol complex values) S_(TOT)=2^(N+2)−1in a frequency frame of M_(MFS)=2^(N+1)+1 main mode frequency pulses;and

the number of equations, which represents also the overall number M_(TS)of the samples in time domain, which is given by

$M_{TS} = {{\left( {1 + \frac{N\left( {N + 1} \right)}{2}} \right)2^{N + 1}} + 1.}$

More in detail, in order to solve the equation system at the receptionside, a reception matrix [[GFFT]] is used by the symbol extraction unit800, which reception matrix [[GFFT]] is derived from the transmissionmatrix [[GIFFT]] through a generalized inversion technique, such as thepseudo-inverse technique.

In mathematical terms, given the transmission matrix [[GIFFT]] withM_(TS)xS_(TOT) complex coefficients, and given also the vector [S] ofthe S_(TOT) symbol complex values to be transmitted, at transmissionside there results that:

[[GIFFT]] [S]=[TTU]

where [TTU] denote the vector of the M_(TS) complex values of the timesamples of a digital time signal outputted by the frequency twisted modegeneration unit 700.

Let us now consider the reception side, where it is useful to use ageneralized inversion technique, such as the pseudo-inverse technique,to invert the foregoing matrix equation:

[[GIFFT]]^(T) [[GIFFT]] [S]=[[GIFFT]]^(T) [TTU],

and thence

[S]=([[GIFFT]]^(T) [[GIFFT]])⁻¹ [[GIFFT]]^(T)[TTU],   (1)

where [[GIFFT]]^(T) denotes the transpose of the matrix [[GIFFT]], and([[GIFFT]]^(T) [[GIFFT]])⁻¹ denotes the operation of inversion of thesquare matrix resulting from the multiplication [[GIFFT]]^(T) [[GIFFT]].

In particular, at reception side [S] becomes the vector of the S_(TOT)unknown symbol complex values to be determined by the symbol extractionunit 800, and [TTU] becomes the vector of the M_(TS) complex values ofthe time samples determined by the symbol extraction unit 800 on thebasis of an incoming digital signal portion.

Condition for the existence of a set of solutions for the unknown vector[S] is that the square matrix resulting from the multiplication[GIFFT]]^(T) [[GIFFT]] has a determinant different than zero, i.e., inmathematical terms,

det ([[A]]^(T) [A])≠0.   (2)

Therefore, if the transmission matrix [[GIFFT]] is designed so as tosatisfy the condition (2), then the S_(TOT) unknown symbol complexvalues can be determined by the symbol extraction unit 800 by solvingthe equation system resulting from the matrix equation (1).

Thence, the reception matrix [[GFFT]], which is a non-Hermitian matrix,can be defined as:

[[GFFT]]=([[GIFFT]]^(T)[[GIFFT]])⁻¹ [[GIFFTA]]^(T).

In this respect, FIG. 38 schematically shows an example of square matrixresulting from the multiplication [[GIFFT]]^(T) [[GIFFT]] on theassumption that modes up to ±1 are used. In particular, the matrix shownin FIG. 38 includes cells which are blank or grey, wherein the greycells represent the matrix cells actually occupied by coefficients,while the blank cells represent the matrix cells not occupied by anycoefficient. This representation of the matrix stems from the fact thatthe FIG. 38 is mainly intended to show the matrix structure (and not thematrix coefficients).

The condition (2) is satisfied more easily in the frequency twist casethan in the time twist one, as it can inferred by looking at the shapeof the time signals. The main reason for such a behaviour is based onthe fact that a frequency function is intrinsically complex, while atime signal is real. In other words, the square matrix resulting fromthe multiplication [[GIFFT]]^(T) [[GIFFT]] is much more robust than thesimilar matrix obtained in the case of time twisted waves.

It is important to note that the determinant is well sized and does notrequire an increase of the bandwidth as in the time twisted wave case.In fact, changing from 19 to 18 samples the determinant relative valuechanges from 1 to about 0.1, which are both values valid for the matrixinversion.

Ideally, the use of the cyclic prefix allows interference level to belimited close to zero. This is true when a large number of side lobesare present outside the useful bandwidth. For the TFUs the bandwidth islimited to the first side-lobe of the frequency pattern, therefore theinterference level is of the order of about −30/−35 dB. This can beconsidered self-generated noise due to inter-frame interference.

The presence of self-generated noise produces a limitation on theinformation transmission capacity when the E_(symbol)/N₀ is very high(namely, higher than 40 dB), as shown in FIG. 34. This limitation ispresent in all the cases where the physical resource is reused (e.g.orthogonal polarization limit 35-40 dB).

Sizing and configuration of a transmitter and a receiver using frequencytwisted waves according to the present invention can be considered aninnovative updating of the OFDM, OFDMA and COFDM (i.e., Coded OFDM)architectures.

In this respect, FIG. 39 schematically shows a multilayer architecturewherein the frame structure of the frequency twisted waves is embeddedin a traditional OFDM architecture.

The proposed architecture allows the OFDM basic structure to be usedwith the additional layer of frequency twisted waves (including the sizeand the references of the frequency twisted wave frame, i.e., thefrequency slot positions, their phases and the association of thesefrequencies with the transmitted symbols, as described in detail in theforegoing).

The advantage of frequency twisted waves with respect to time twistedwaves is evident in this aspect; in fact, for frequency twisted wavesthere is no need to build up a dedicated “space reference system” as inthe case of time twist and this is due to the important considerationthat OFDM and similar transmission techniques are already “block signaltransmission” techniques (i.e., implement simultaneous transmission ofsignals using IFFT).

The size of transmission block is increased by a factor related to thenumber of frequency twisted modes used. In fact, as previouslyexplained, each twisted frequency mode ±n exploits a sequence of 2^(N+1)additional frequency carriers (where ±1V are the highest modes used)positioned at

${B_{S}\left( {\frac{2^{n} - 1}{2^{n}} + k} \right)},$

where0≦k≦2^(N+1)−1.

The receiver (in particular, the symbol extraction unit 800) handles anumber of unknowns S_(TOT) smaller than the number of equations M_(TS)(as previously explained), this implies the use of the pseudo-inversetechnique and an increase of the computational complexity with respectto the usual OFDM block signal computation, which, as is known, producessquare matrixes L_(SF)xL_(SF), where L_(SF) is the length of the superframe.

Instead, in the case of frequency twisted waves, assuming the same superframe length L_(SF) and a frame length L_(TFU) equal to 2^(N+1)+1, thenumber of equation for said super frame is:

${{M_{TS}\frac{L_{SF}}{2^{N + 1} + 1}} = {\left\lbrack {{\left( {1 + \frac{N\left( {N + 1} \right)}{2}} \right)2^{N + 1}} + 1} \right\rbrack \frac{L_{SF}}{2^{N + 1} + 1}}},$

where, if N=2 and L_(SF)=2016, the number of equations is 7392 and thenumber of the unknowns is given by

${\frac{2^{N + 2} + 1}{2^{N + 1} + 1}L_{SF}} = 3808.$

The increased complexity factor of the matrix operations is given by theratio between the number of operations of twisted waves and the numberof OFDM operations:

$\frac{{\left( {\frac{2^{N + 2} + 1}{2^{N + 1} + 1}L_{SF}} \right)\left\lbrack {{\left( {1 + \frac{N\left( {N + 1} \right)}{2}} \right)2^{N + 1}} + 1} \right\rbrack}\frac{L_{SF}}{2^{N + 1} + 1}}{\left( L_{SF} \right)^{2}} = {6.1.}$

In this respect, FIG. 40 shows computational complexity of the presentinvention and frequency reuse according to the latter as a function of N(where, as previously said, ±N are the highest twisted frequency modesused). From FIG. 40 it is evident that a reasonable compromise isobtained with N=2, with a very good frequency reuse and a limitedincrease in computational complexity.

The introduction of an additional layer in the super frame organizationis somewhat limiting the possibility of OFDM adapting itself to thechannel characteristics; i.e., in a traditional OFDM frame theadaptability is given by the single carrier bandwidth B_(S), while forthe frequency twisted wave case the adaptability is given by (2^(N+1)+1)B_(S). This is a limitation on the system adaptability and has the sametrend of the computational complexity. In this respect, FIG. 41schematically illustrates flexibility in using OFDM modularity, complexequation number and implementation criticality of the present inventionas a function of N (where, as previously said, ±N are the highesttwisted frequency modes used).

Some features of the present invention are briefly summarized herebelow:

due the structure of the OFDM signal there is no additional noise due tothe introduction of frequency twisted waves;

the OFDM cyclic prefix includes the equivalent cyclic prefix necessaryfor frequency twisted waves; anyway, it is clear that, if the cyclicprefix is fully used for OFDM, it should be accordingly increased; and

there is no practical advantage of performance in using frequencytwisted mode higher than ±3, but, on the contrary, computationalcomplexity grows quite rapidly.

As explained in the foregoing, the implementation of the frequencytwisted waves according to the present invention can be regarded as anapproximation of the frequency Hilbert transform. This fact implies, onone side, a bandwidth increase, and, on the other side, the presence ofan absolute limitation on the increase in frequency reuse, which islower than two. In this respect, the following TABLE II lists somefeatures related to the use of frequency twisted waves according to thepresent invention.

TABLE II Parameter value Parameter (considering using approximate valueParameter up to modes ±N) for N = 2 Frequency reuse$\frac{2^{N + 2} - 1}{2^{N + 1} + 1}$ 1.67 Vestigial time intervalincrease $\frac{2^{N + 2} + 3}{2^{N + 2} + 2}$ 1.056 Total framebandwidth/symbol bandwidth$\frac{B_{F}}{B_{S}} = \frac{2^{N + 2} + 3}{2}$ 9.5 Super Frame loss <1%0.99 Additional bandwidth noise (dB)$10\mspace{11mu} {\log \left( \frac{2^{N + 3} + 3}{2^{N + 3} + 2} \right)}{dB}$0.25 dB Digitalization noise < −30 dB phase error $\frac{N}{2^{N} - 1}$9 bits Maximum inter- <−19-3N dB <−25 dB frame interference (dB)

For N=3, the frame length is smaller than 32 symbols, the necessarynumber of bits is about 10, the increase of the thermal noise is closeto 0 dB, and the frequency reuse close to 1.7.

As far as practical implementation of the present invention isconcerned, the frequency twisted mode generation unit 700 based on GIFFTand the symbol extraction unit 800 based on GFFT are preferablyimplemented by means of Field-Programmable Gate Array (FPGA),Application-Specific Integrated Circuit (ASIC), and Software DefinedRadio (SDR) technologies.

From the foregoing, it may be immediately appreciated that the presentinvention allows to increase frequency reuse and transmission capacityby exploiting an original application of the Hilbert transform infrequency domain.

The present invention can be considered very interesting and almostrevolutionary to develop a new theory for digital communications beyondthe classical approach based on analytical signals.

In particular, as previously explained in detail, according to thepresent invention radio vorticity is considered as a way to approximatethe Hilbert transform and is applied in frequency domain so as togenerate independent radio channels within one and the same bandwidth.These channels have an available bandwidth decreasing with the radiovorticity mode number and the total bandwidth advantage is growing as1/2^(N), limited by 2, which represents the maximum possible use of theimaginary channel of the Hilbert transform.

From a mathematical (and physical) perspective, thisHilbert-transform-based approach is very similar to an interferometrymeasurement performed in frequency instead of in geometrical space.

The present invention can be advantageously exploited, in general, inall kinds of radio communications, and, in particular, in radiocommunications based, in general, on OFDM and/or OFDMA, and,specifically, on LTE and/or WiMAX.

Finally, it is worth noting that a combined use of frequency twistaccording to the present invention and time twist according toPCT/FR2013/052636 is particularly advantageous in asymmetrical radiocommunications systems, such as mobile radio communications systems, forexample based on LTE and/or WiMAX. In fact, in such a scenario,frequency twist according to the present invention can be advantageouslyapplied to the Forward channel from a Base Station to a mobile device,while time twist according to PCT/FR2013/052636 can be advantageouslyapplied to the Return channel from a mobile device to a Base Station.

In conclusion, it is clear that numerous modifications and variants canbe made to the present invention, all falling within the scope of theinvention, as defined in the appended claims.

1. A radio communications method comprising carrying out, by atransmitter, the following steps: a) providing a digital time signalcarrying digital symbols to be transmitted; and b) transmitting a radiofrequency signal carrying said digital time signal; the method furthercomprising carrying out, by a receiver, the following steps: c)receiving the radio frequency signal transmitted by the transmitter; d)processing the received radio frequency signal so as to obtain acorresponding incoming digital signal; and e) extracting, from theincoming digital signal, the digital symbols carried by said incomingdigital signal; wherein said digital time signal carrying the digitalsymbols to be transmitted results from an approximation of the Hilberttransform in frequency domain, which approximation is based on afrequency main mode and one or more frequency twisted modes, whereinsaid frequency main and twisted modes carry, each, respective digitalsymbols to be transmitted.
 2. The method of claim 1, wherein the digitaltime signal is time-limited, carries a limited sequence of digitalsymbols to be transmitted, and results from: main mode frequency samplescarrying respective digital symbols of said limited sequence via afrequency main mode; and twisted mode frequency samples carrying theother digital symbols of said limited sequence via one or more frequencytwisted modes, wherein each frequency twisted mode is a complex harmonicmode that is orthogonal to the frequency main mode and to any otherfrequency twisted mode used.
 3. The method of claim 2, wherein the mainmode frequency samples are at main mode frequencies spaced apart by apredetermined frequency spacing; and wherein the twisted mode frequencysamples comprise, for a frequency twisted mode, respective twisted modefrequency samples at corresponding twisted mode frequencies that: arerelated to said frequency twisted mode; are spaced apart by saidpredetermined frequency spacing; and are different from the main modefrequencies.
 4. The method of claim 3, wherein the one or more frequencytwisted modes comprise 2N frequency twisted modes each identified by arespective integer index n that is comprised between −N and +N and isdifferent from zero, N denoting an integer higher than zero; wherein thelimited sequence of digital symbols to be transmitted comprises S_(TOT)digital symbols, S_(TOT) being equal to 2^(N+2)−1; wherein the frequencymain mode carries M_(MFS) of said S_(TOT) digital symbols by means ofM_(MFS) main mode frequency samples at corresponding main modefrequencies, that are spaced apart by said predetermined frequencyspacing and that range from B_(S) to M_(MFS) times B_(S), B_(S) denotingsaid predetermined frequency spacing and M_(MFS) being equal to2^(N+1)+1; wherein said 2N frequency twisted modes carry theS_(TOT)-M_(MFS) digital symbols not carried by the frequency main mode;and wherein each frequency twisted mode n carries 2^(N−|n|) respectivedigital symbol(s) by means of 2^(N+1) respective twisted mode frequencysamples at corresponding twisted mode frequencies, that are spaced apartby said predetermined frequency spacing and that are located, infrequency domain, at${B_{S}\left( {\frac{2^{n} - 1}{2^{n}} + k} \right)},$ where kdenotes an integer ranging from zero to 2^(N+19)−1, or from one to2^(N+1).
 5. The method of claim 4, wherein each of said S_(TOT) digitalsymbols to be transmitted is represented by a respective symbol complexvalue; and wherein, for each frequency twisted mode n, the 2^(N+1)respective twisted mode frequency samples comprise, for each of the2^(N−|n|) respective digital symbol(s), 2^(|n|+1) frequency samples,that: carry said digital symbol; are at frequencies that are located, infrequency domain, at${B_{S}\left\lbrack {\frac{2^{n} - 1}{2^{n}} + \left( {k^{*} + {i \cdot 2^{{n} + 1}}} \right)} \right\rbrack},$where k* denotes an integer ranging from zero to 2^(|n|+1)−1, or fromone to 2^(|n|+1), and where i is an index that identifies said digitalsymbol and is comprised between zero and 2^(N−|n|)−1 and have, each, arespective complex value obtained by multiplying the symbol complexvalue representing said digital symbol by a respective complex factorrelated to said frequency twisted mode n and to the frequency of saidfrequency sample.
 6. The method of claim 5, wherein, for each frequencytwisted mode n and for each of the 2^(N−|n|) respective digitalsyrnbol(s), the 2^(|n|+1) respective frequency samples carrying saiddigital symbol have, each, a respective complex value obtained bymultiplying the symbol complex value representing said digital symbol bya respective complex factor which: if n is higher than zero, is equal to$\frac{^{{+ j}\; {k \cdot \frac{\pi}{2^{n}}}}}{2^{\frac{{n} + 1}{2}}}$or, if n is lower than zero, is equal to$\frac{^{{- j}\; {k \cdot \frac{\pi}{2^{n}}}}}{2^{\frac{{n} + 1}{2}}}$where j denotes the imaginary unit.
 7. The method according to claim 4,wherein said step a) includes providing the digital time signal by usinga predefined transmission matrix that relates the S_(TOT) digitalsymbols to be transmitted to time samples of the digital time signalthrough coefficients related to a transform from frequency domain totime domain of the main mode frequency samples and the twisted modefrequency samples; and wherein said step e) includes extracting thedigital symbols carried by the incoming digital signal by using areception matrix derived from the predefined transmission matrix.
 8. Themethod of claim 7, wherein the predefined transmission matrix is suchthat the matrix resulting from the multiplication of the transpose ofsaid predefined transmission matrix and said predefined transmissionmatrix has a determinant different from zero; and wherein the receptionmatrix is derived from the predefined transmission matrix through apseudo-inverse technique.
 9. The method of claim 8, wherein thereception matrix is computed on the basis of the following formula:[[GFFT]]=([[GIFFT]]^(T) [[GIFFT]])⁻¹ [[GIFFT]]^(T), where [[GFFT]]denotes the reception matrix, [[GIFFT]] denotes the predefinedtransmission matrix, [[GIFFT]]^(T) dentoes the transpose of thepredefined transmission matrix, and ([[GIFFT]]^(T) [[GIFFT]])⁻¹ denotesthe operation of inversion of the matrix resulting from themultiplication of the transpose of the predefined transmission matrixand the predefined transmission matrix.
 10. The method according toclaim 7, wherein the digital time signal comprises a number of timesamples equal to${{\left\lbrack {1 + \frac{N\left( {N + 1} \right)}{2}} \right\rbrack 2^{N + 1}} + 1};$and wherein the predefined transmission matrix comprises MT_(ST)XS_(TOT)coefficients, M_(TS) denoting said number of time samples of the digitaltime signal.
 11. The radio communications method according to claim 2,wherein the main mode frequency samples are frequency samples ofOrthogonal Frequency-Division Multiplexing (OFDM) type, or of OrthogonalFrequency-Division Multiple Access (OFDMA) type.
 12. The radiocommunications method according to claim 2, wherein said step a)includes: providing a first digital time signal resulting from the mainmode frequency samples and the twisted mode frequency samples; andproviding a second digital time signal which includes a cyclic prefixfollowed by the first digital time signal, wherein the cyclic prefix isa replica of an end portion of said first digital time signal; andwherein said step b) includes transmitting a radio frequency signalcarrying the second digital time signal.
 13. A radio communicationssystem comprising a transmitter and a receiver; wherein the transmitteris configured to carry out the steps a) and b) of the radiocommunications method claimed in claim 1, and the receiver is configuredto carry out the steps c), d) and e) of the radio communications method.14. A system for radio communications configured to carry out the stepsa) and b) of the radio communications method claimed in claim
 1. 15. Ahardware component comprising software code portions which are:executable by a processor of a device or system for radiocommunications; and such that to cause, when executed, said device orsystem to become configured to carry out the steps a) and b) of theradio communications method claimed in claim
 1. 16. A system for radiocommunications configured to: radio communicate with another device orsystem designed to carry out the steps a) and b) of the radiocommunications method claimed in claim 1; and carry out the steps c), d)and e) of the radio communications method.
 17. A hardware componentcomprising software code portions which are: executable by a processorof a first device or system designed to radio communicate with a seconddevice or system designed to carry out the steps a) and b) of the radiocommunications method claimed in claim 1; and such that to cause, whenexecuted, said second device or system to become configured to carry outthe steps c), d) and e) of the radio communications method.